Deck 12: Applications of the Derivative

Question 1

Find the location and value of each local extremum for the function.

-

A) $(-2,0),(-1,2),(2,1)$
B) $(-3,-1),(-2,0),(2,1)$
C) $(-3,-1),(-1,2),(2,1)$
D) $(-3,-1),(-1,2),(-2,0)$

Answer 1

$(-3,-1),(-1,2),(2,1)$

Question 2

Find the location and value of each local extremum for the function.

-

A) $(3,-2)$
B) $(3,-2),(6,0)$
C) $(0,0),(3,-2),(6,0)$
D) $(0,0),(6,0)$

Answer 2

$(3,-2)$

Question 3

Find the location and value of each local extremum for the function.

-

A) $(2,0)$
B) None
C) $(-2,3)$
D) $(-2,3),(2,0)$

Answer 3

$(-2,3),(2,0)$

Question 4

Find the location and value of each local extremum for the function.

-

A) $(1,0)$
B) $(1,2)$
C) None
D) $(0,1)$

Question 5

Find the location and value of each local extremum for the function.

-

A) $(2,1),(-2,-1)$
B) $(2,1)$
C) None
D) $(-2,-1)$

Question 6

Find the location and value of each local extremum for the function.

-

A) None
B) $(-2,5),(0,0),(2,5)$
C) $(-2,5),(2,5)$
D) $(0,0)$

Question 7

Find the location and value of each local extremum for the function.

-

A) None
B) $(0,2)$
C) $(-2,0)$
D) $(0,2),(-2,0)$

Question 8

Find the location and value of each local extremum for the function.

-

A) $(-3.5,0),(-2,2),(1.5,0),(3.1,2)$
B) $(-3.5,0),(1.5,0)$
C) $(-2,2),(1.5,0)$
D) None

Question 9

Find the location and value of each local extremum for the function.

-

A) $(-3,0),(3.75,0)$
B) $(1.5,-1)$
C) $(-6,3),(1.5,-1),(4.2,2)$
D) None

Question 10

Find the location and value of each local extremum for the function.

-

A) $(-5.5,-3),(-3.5,-1.5),(3.5,1.5),(5.5,3)$
B) $(-3.5,-1.5),(3.5,1.5)$
C) $(-5.5,-3),(5.5,3)$
D) None

Question 11

Identify the intervals where the function is changing as requested.

-Increasing

A) $(-3, \infty)$
B) $(-3,3)$
C) $(-2, \infty)$
D) $(-2,2)$

Question 12

Identify the intervals where the function is changing as requested.

-Decreasing

A) $(-\infty, 0)$
B) $(0,3)$
C) $(-1,0)$
D) $(3, \infty)$

Question 13

Identify the intervals where the function is changing as requested.

-Increasing

A) $(3, \infty)$
B) $(-2, \infty)$
C) $(-2,0)$
D) $(3,6)$

Question 14

Identify the intervals where the function is changing as requested.

-Increasing

A) $(-1,2)$
B) $(-2,-1) \cup(2, \infty)$
C) $(-2,-1)$
D) $(-1, \infty)$

Question 15

Identify the intervals where the function is changing as requested.

-Increasing

A)
B) $(0,5)$
C) $(1,6)$
D) $(0,6)$

Question 16

Identify the intervals where the function is changing as requested.

-Increasing

A) $(-1,0)$
B) $(0,3)$
C) $(-\infty,-1)$
D) $(-\infty, 0)$

Question 17

Identify the intervals where the function is changing as requested.

-Decreasing

A) $(-\infty,-2)$
B) $(-3,-2)$
C) $(-\infty,-3)$
D) $(0,-2)$

Question 18

Identify the intervals where the function is changing as requested.

-Decreasing

A) $(5,1)$
B) $(5,12)$
C) $(6,1)$
D) $(6,12)$

Question 19

Identify the intervals where the function is changing as requested.

-Decreasing

A) $(0,3)$
B) $(-\infty,-2)$
C) $(0,-2)$
D) $(-\infty, 3)$

Question 20

Identify the intervals where the function is changing as requested.

-Decreasing

A) $(-1,2)$
B) $(2,1)$
C) $(2,-1)$
D) $(1,2)$

Question 21

Find the largest open interval where the function is changing as requested.

-Increasing $y=7 x-5$

A) $(-\infty, 7)$
B) $(-5,7)$
C) $(-\infty, \infty)$
D) $(-5, \infty)$

Question 22

Find the largest open interval where the function is changing as requested.

-Increasing $f(x)=\frac{1}{4} x^{2}-\frac{1}{2} x$

A) $(-\infty,-1)$
B) $(-\infty, \infty)$
C) $(1, \infty)$
D) $(-1,1)$

Question 23

Find the largest open interval where the function is changing as requested.

-Increasing $f(x)=x^{2}-2 x+1$

A) $(0, \infty)$
B) $(-\infty, 1)$
C) $(1, \infty)$
D) $(-\infty, 0)$

Question 24

Find the largest open interval where the function is changing as requested.

-Increasing $y=\left(x^{2}-9\right)^{2}$

A) $(3, \infty)$
B) $(-3,0)$
C) $(-3,3)$
D) $(-\infty, 0)$

Question 25

Find the largest open interval where the function is changing as requested.

-Increasing $f(x)=\frac{1}{x^{2}+1}$

A) $(1, \infty)$
B) $(-\infty, 0)$
C) $(0, \infty)$
D) $(-\infty, 1)$

Question 26

Find the largest open interval where the function is changing as requested.

-Decreasing $f(x)=|x-8|$

A) $(8, \infty)$
B) $(-\infty, 8)$
C) $(-\infty,-8)$
D) $(-8, \infty)$

Question 27

Find the largest open interval where the function is changing as requested.

-Decreasing $y=\frac{1}{x^{2}}+7$

A) $(7, \infty)$
B) $(-7,7)$
C) $(0, \infty)$
D) $(-7,0)$

Question 28

Find the largest open interval where the function is changing as requested.

-Decreasing $f(x)=x^{3}-4 x$

A) $\left(-\frac{2 \sqrt{3}}{3}, \frac{2 \sqrt{3}}{3}\right)$
B) $\left(\frac{2 \sqrt{3}}{3}, \infty\right)$
C) $(-\infty, \infty)$
D) $\left(-\infty,-\frac{2 \sqrt{3}}{3}\right)$

Question 29

The graph of the derivative function $f^{\prime}$ is given. Find the critical numbers of the function $f$ .

-

A) 1
B) 0.5
C) 0
D) 0,1

Question 30

The graph of the derivative function $f^{\prime}$ is given. Find the critical numbers of the function $f$ .

-

A) $-1.5,1.5$
B) $-3,3$
C) none
D) 0

Question 31

The graph of the derivative function $f^{\prime}$ is given. Find the critical numbers of the function $f$ .

-

A) 2
B) 0,2
C) $-2,2$
D) 0

Question 32

The graph of the derivative function $f^{\prime}$ is given. Find the critical numbers of the function $f$ .

-

A) - $1,0,1$
B) $-1,1$
C) -1
D) 0

Question 33

The graph of the derivative function $f^{\prime}$ is given. Find the critical numbers of the function $f$ .

-

A) 0,2
B) $\frac{2}{3}, 2$
C) $0, \frac{2}{3}, 2$
D) none

Question 34

Determine the location of each local extremum of the function.

- $f(x)=x^{3}+\frac{7}{2} x^{2}+12 x+4$

A) Local maximum at 3 ; local minimum at 4
B) Local maximum at -4 ; local minimum at -3
C) No local extrema
D) Local extremum at 3.5

Question 35

Determine the location of each local extremum of the function.

- $f(x)=-x^{3}-1.5 x^{2}+36 x+3$

A) Local maximum at 4 ; local minimum at -3
B) Local maximum at -4 ; local minimum at 3
C) Local maximum at 3 ; local minimum at -4
D) Local maximum at -3 ; local minimum at 4

Question 36

Determine the location of each local extremum of the function.

- $f(x)=\frac{x^{4}}{4}-\frac{4}{3} x^{3}-\frac{9}{2} x^{2}+36 x+4$

A) Local maxima at -3 and 4 ; local minimum at 3
B) Local maximum at -3 ; local minimum at 4
C) Local maxima at 3 and -4 ; local minimum at 3
D) Local maximum at 3 ; local minima at -3 and 4

Question 37

Determine the location of each local extremum of the function.

- $f(x)=x^{3}+3.5 x^{2}+2 x-3$

A) Local maximum at $\frac{1}{3}$ ; local minimum at 2
B) Local maximum at $-\frac{2}{3}$ ; local minimum at -1
C) Local maximum at -2 ; local minimum at $\frac{-1}{3}$
D) Local maximum at 1 ; local minimum at 0.67

Question 38

Determine the location of each local extremum of the function.

- $f(x)=x^{3}-9 x^{2}+27 x+1$

A) Local minimum at 3
B) Local maximum at 3
C) Local maximum at 3 ; local minimum at -3
D) No local extrema

Question 39

Use the first derivative test to determine the location of each local extremum and the value of the function at thatextremum.

- $f(x)=(4-2 x)^{3 / 5}-4$

A) No local extrema
B) Local maximum at $(2,-4)$
C) Local minimum at $(2,-4)$
D) Local minimum at $(0,-4)$

Question 40

Use the first derivative test to determine the location of each local extremum and the value of the function at thatextremum.

- $f(x)=\frac{x^{2}}{x^{2}+5}$

A) Local maximum at $(0,0)$
B) No local extrema
C) Local minimum at $(0,0)$
D) Local minimum at $(5,0.83333333)$

Question 41

Use the first derivative test to determine the location of each local extremum and the value of the function at thatextremum.

- $f(x)=3 x e^{-x}$

A) No local extrema
B) Local minimum at $\left(1, \frac{3}{\mathrm{e}}\right)$
C) Local maximum at $\left(1, \frac{3}{\mathrm{e}}\right)$
D) Local minimum at $\left(3, \frac{3}{\mathrm{e}}\right)^{\text {) }}$

Question 42

Use the first derivative test to determine the location of each local extremum and the value of the function at thatextremum.

- $f(x)=\frac{x^{2}-8 x+16}{x-5}$

A) No local extrema
B) Local maximum at $(4,0)$ ; local minimum at $(6,4)$
C) Local maximum at $(0,16)$ ; local minima at $(4,0)$ and $(14,11.11)$
D) Local maximum at $(6,4)$ ; local minimum at $(4,0)$

Question 43

Use the maximum/minimum finder on a graphing calculator to determine the approximate location of all local extrema.

- $f(x)=0.1 x^{3}-15 x^{2}+46 x-86$

A) Approximate local maximum at -98.442 ; approximate local minimum at -1.558
B) Approximate local maximum at 1.558 ; approximate local minimum at 98.442
C) Approximate local minimum at 1.558 ; approximate local maximum at 98.442
D) Approximate local minimum at -98.442; approximate local maximum at -1.558

Question 44

Use the maximum/minimum finder on a graphing calculator to determine the approximate location of all local extrema.

- $f(x)=0.1 x^{4}-x^{3}-15 x^{2}+59 x+14$

A) Approximate local maximum at 1.735; approximate local minima at -6.777 and 12.542
B) Approximate local maximum at 1.801; approximate local minima at -6.723 and 12.642
C) Approximate local maximum at 1.817; approximate local minima at -6.837 and 12.465
D) Approximate local maximum at 1.815 ; approximate local minima at -6.778 and 12.597

Question 45

Use the maximum/minimum finder on a graphing calculator to determine the approximate location of all local extrema.

- $f(x)=x^{4}-3 x^{3}-21 x^{2}+74 x-2$

A) Approximate local maximum at 1.577; approximate local minima at -3.108 and 3.721
B) Approximate local maximum at 1.536 ; approximate local minima at -3.157 and 3.69
C) Approximate local maximum at 1.604; approximate local minima at -3.089 and 3.735
D) Approximate local maximum at 1.671 ; approximate local minima at -3.163 and 3.704

Question 46

Use the maximum/minimum finder on a graphing calculator to determine the approximate location of all local extrema.

- $f(x)=x^{4}-4 x^{3}-53 x^{2}-86 x+5$

A) Approximate local maximum at -0.944 ; approximate local minima at -3.192 and 7.136
B) Approximate local maximum at 1.02 ; approximate local minima at -3.167 and 7.046
C) Approximate local maximum at 0.852 ; approximate local minima at -3.234 and 7.127
D) Approximate local maximum at 0.935 ; approximate local minima at -3.119 and 7.198

Question 47

Use the maximum/minimum finder on a graphing calculator to determine the approximate location of all local extrema.

- $f(x)=x^{5}-15 x^{4}-3 x^{3}-172 x^{2}+135 x+0.002$

A) Approximate local maximum at 0.353 ; approximate local minimum at -12.638
B) Approximate local maximum at 0.29 ; approximate local minima at -0.572 and -12.568
C) Approximate local maximum at 0.379 ; approximate local minimum at 12.565
D) Approximate local maximum at 0.379 ; approximate local minima at -0.472 and 12.565

Question 48

Use the maximum/minimum finder on a graphing calculator to determine the approximate location of all local extrema.

- $f(x)=0.1 x^{5}+5 x^{4}-8 x^{3}-15 x^{2}-6 x-35$

A) Approximate local maxima at -41.038 and -0.368 ; approximate local minima at -0.564 and 1.858
B) Approximate local maxima at -41.075 and -0.343 ; approximate local minima at -0.616 and 2.021
C) Approximate local maxima at -41.132 and -0.273 ; approximate local minima at -0.547 and 1.952
D) Approximate local maxima at -41.207 and -0.249 ; approximate local minima at -0.513 and 1.976

Question 49

Use the maximum/minimum finder on a graphing calculator to determine the approximate location of all local extrema.

- $f(x)=0.01 x^{5}-x^{4}+x^{3}+8 x^{2}-7 x+87$

A) Approximate local maxima at -1.861 and 2.247 ; approximate local minimum at 0.423
B) Approximate local maxima at -1.85 and 2.165 ; approximate local minima at 0.445 and 79.11
C) Approximate local maxima at -1.864 and 2.282 ; approximate local minima at 0.373 and 79.195
D) Approximate local maxima at -1.861 and 2.247 ; approximate local minima at 0.423 and 79.192

Question 50

Solve each problem.

-If the price charged for a bolt is $p$ cents, then $x$ thousand bolts will be sold in a certain hardware store, where $p=125-\frac{x}{14}$ . How many bolts must be sold to maximize revenue?

A) 875 thousand bolts
B) 1750 thousand bolts
C) 875 bolts
D) 1750 bolts

Question 51

Solve each problem.

-The price $P$ of a certain computer system decreases immediately after its introduction and then increases. If the price $\mathrm{P}$ is estimated by the formula $\mathrm{P}=130 \mathrm{t}^{2}-2500 t+6900$ , where $\mathrm{t}$ is the time in months from its introduction, find the time until the minimum price is reached.

A) 19.2 months
B) 38.5 months
C) 12.5 months
D) 9.6 months

Question 52

Solve each problem.

-A rectangular field is to be enclosed on four sides with a fence. Fencing costs $\$ 8$ per foot for two opposite sides, and $\$ 4$ per foot for the other two sides. Find the dimensions of the field of area $800 \mathrm{ft}^{2}$ that would be the cheapest to enclose.

A) $40 \mathrm{ft} @ \$ 8$ by $20 \mathrm{ft} @ \$ 4$
B) $20 \mathrm{ft} @ \$ 8$ by $40 \mathrm{ft} @ \$ 4$
C) $14.1 \mathrm{ft} @ \$ 8$ by $56.6 \mathrm{ft} @ \$ 4$
D) $56.6 \mathrm{ft} @ \$ 8$ by $14.1 \mathrm{ft} @ \$ 4$

Question 53

Solve each problem.

-The cost of a computer system increases with increased processor speeds. The cost $C$ of a system as a function of processor speed is estimated as $C=12 S^{2}-9 S+1000$ , where $S$ is the processor speed in MHz. Find the processor speed for which cost is at a minimum.

A) $0.4 \mathrm{MHz}$
B) $0.5 \mathrm{MHz}$
C) $3 \mathrm{MHz}$
D) $7.5 \mathrm{MHz}$

Question 54

Solve each problem.

-The velocity of a particle (in $\mathrm{ft} / \mathrm{s}$ ) is given by $\mathrm{v}=\mathrm{t}^{2}-8 \mathrm{t}+3$ , where $\mathrm{t}$ is the time (in seconds) for which it has traveled. Find the time at which the velocity is at a minimum.

A) $3 \mathrm{~s}$
B) $1.5 \mathrm{~s}$
C) $8 \mathrm{~s}$
D) $4 \mathrm{~s}$

Question 55

Solve each problem.

-Find the dimensions that produce the maximum floor area for a one-story house that is rectangular in shape and has a perimeter of $157 \mathrm{ft}$ .

A) $13.08 \mathrm{ft} \times 39.25 \mathrm{ft}$
B) $78.5 \mathrm{ft} \times 78.5 \mathrm{ft}$
C) $39.25 \mathrm{ft} \times 39.25 \mathrm{ft}$
D) $39.25 \mathrm{ft} \times 157 \mathrm{ft}$

Question 56

Solve each problem.

-An architect needs to design a rectangular room with an area of $91 \mathrm{ft}^{2}$ . What dimensions should she use in order to minimize the perimeter?

A) $9.54 \mathrm{ft} \times 9.54 \mathrm{ft}$
B) $9.54 \mathrm{ft} \times 22.75 \mathrm{ft}$
C) $18.2 \mathrm{ft} \times 91 \mathrm{ft}$
D) $22.75 \mathrm{ft} \times 22.75 \mathrm{ft}$

Question 57

Solve each problem.

-A piece of molding $182 \mathrm{~cm}$ long is to be cut to form a rectangular picture frame. What dimensions will enclose the largest area?

A) $13.49 \mathrm{~cm} \times 45.5 \mathrm{~cm}$
B) $36.4 \mathrm{~cm} \times 36.4 \mathrm{~cm}$
C) $45.5 \mathrm{~cm} \times 45.5 \mathrm{~cm}$
D) $13.49 \mathrm{~cm} \times 13.49 \mathrm{~cm}$

Question 58

Solve each problem.

-Find two numbers whose sum is 440 and whose product is as large as possible.

A) 219 and 221
B) 1 and 439
C) 220 and 220
D) 10 and 430

Question 59

Solve each problem.

-Find the dimensions of the rectangular field of maximum area that can be made from $140 \mathrm{~m}$ of fencing material.

A) $35 \mathrm{~m}$ by $105 \mathrm{~m}$
B) $70 \mathrm{~m}$ by $70 \mathrm{~m}$
C) $14 \mathrm{~m}$ by $126 \mathrm{~m}$
D) $35 \mathrm{~m}$ by $35 \mathrm{~m}$

Question 60

Evaluate $\mathrm{f}^{\prime \prime}(\mathrm{c})$ at the point.

- $f(x)=\frac{3 x-4}{4 x-3}, c=1$

A) $\mathrm{f}^{\prime \prime}(1)=32$
B) $\left.f^{\prime \prime} 1\right)=7$
C) $\mathrm{f}^{\prime \prime}(1)=44$
D) $f^{\prime \prime}(1)=-56$

Question 61

Evaluate $\mathrm{f}^{\prime \prime}(\mathrm{c})$ at the point.

- $f(x)=\frac{3-x}{2 x+3}, c=-2$

A) $f^{\prime \prime}(-2)=-42$
B) $f^{\prime \prime}(-2)=24$
C) $f^{\prime \prime}(-2)=-36$
D) $f^{\prime \prime}(-2)=-9$

Question 62

Evaluate $\mathrm{f}^{\prime \prime}(\mathrm{c})$ at the point.

- $f(x)=\frac{x^{2}+2}{3 x^{2}-1}, c=0$

A) $f^{\prime \prime}(0)=-14$
B) $f^{\prime \prime}(0)=-10$
C) $\mathrm{f}^{\prime \prime}(0)=1$
D) $\mathrm{f}^{\prime \prime}(0)=0$

Question 63

Evaluate $\mathrm{f}^{\prime \prime}(\mathrm{c})$ at the point.

- $f(x)=\left(x^{2}-5\right)\left(x^{3}-5\right), c=1$

A) $f^{\prime \prime}(1)=30$
B) $f^{\prime \prime}(1)=-10$
C) $f^{\prime \prime}(1)=-20$
D) $\mathrm{f}^{\prime \prime}(1)=10$

Question 64

Evaluate $\mathrm{f}^{\prime \prime}(\mathrm{c})$ at the point.

- $f(x)=\left(x^{2}-3 x+2\right)(2 x-6), c=0$

A) $\mathrm{f}^{\prime \prime}(0)=22$
B) $\mathrm{f}^{\prime \prime}(0)=0$
C) $f^{\prime \prime}(0)=-12$
D) $f^{\prime \prime}(0)=-24$

Question 65

Evaluate $\mathrm{f}^{\prime \prime}(\mathrm{c})$ at the point.

- $f(x)=\ln (4 x-3), c=1$

A) $\mathrm{f}^{\prime \prime}(1)=4$
B) $\mathrm{f}^{\prime \prime}(1)=1$
C) $\mathrm{f}^{\prime \prime}(1)=-16$
D) $\mathrm{f}^{\prime \prime}(1)=0$

Question 66

Evaluate $\mathrm{f}^{\prime \prime}(\mathrm{c})$ at the point.

- $f(x)=\ln \left(3 x^{2}-2\right), c=-1$

A) $f^{\prime \prime}(-1)=-1$
B) $f^{\prime \prime}(-1)=-6$
C) $\mathrm{f}^{\prime \prime}(-1)=30$
D) $f^{\prime \prime}(-1)=-30$

Question 67

Evaluate $\mathrm{f}^{\prime \prime}(\mathrm{c})$ at the point.

- $f(x)=e^{-x}, c=0$

A) $\mathrm{f}^{\prime \prime}(0)=0$
B) $\mathrm{f}^{\prime \prime}(0)=-1$
C) $\mathrm{f}^{\prime \prime}(0)=\mathrm{e}$
D) $\mathrm{f}^{\prime \prime}(0)=1$

Question 68

Evaluate $\mathrm{f}^{\prime \prime}(\mathrm{c})$ at the point.

- $f(x)=e^{3 x^{2}-3}, c=1$

A) $f^{\prime \prime}(1)=6$
B) $f^{\prime \prime}(1)=36$
C) $\mathrm{f}^{\prime \prime}(1)=1$
D) $\mathrm{f}^{\prime \prime}(1)=42$

Question 69

Evaluate $\mathrm{f}^{\prime \prime}(\mathrm{c})$ at the point.

- $f(x)=e^{4-x^{2}}, c=2$

A) $f^{\prime \prime}(2)=-4$
B) $f^{\prime \prime}(2)=-20$
C) $\mathrm{f}^{\prime \prime}(2)=1$
D) $\mathrm{f}^{\prime \prime}(2)=14$

Question 70

Solve the problem.

-Find the velocity function $v(t)$ if $s(t)=-7 t^{3}-7 t^{2}-6 t+3$ .

A) $v(t)=-21 t^{2}-6 t-14$
B) $v(t)=-21 t^{2}-14 t-6$
C) $v(t)=-42 t^{2}-14$
D) $v(t)=-42 t^{2}-6 t$

Question 71

Solve the problem.

-Find the acceleration function $a(t)$ if $s(t)=-9 t^{3}-2 t^{2}-6 t-7$ .

A) $a(t)=-27 t^{2}-6 t-4$
B) $a(t)=-27 t^{2}-4 t-6$
C) $a(t)=-54 t-4$
D) $a(t)=-54 t-6$

Question 72

Solve the problem.

-Find the velocity function $v(t)$ if $s(t)=\frac{-3}{4 t+5}$ .

A) $\frac{-144}{(4 t+5)^{3}}$
B) $\frac{12}{(4 t+5)^{2}}$
C) $\frac{-12}{(4 t+5)^{2}}$
D) $\frac{288}{(4 t+5)^{3}}$

Question 73

Solve the problem.

-Find the acceleration function $a(t)$ if $s(t)=\frac{-3}{5 t+5}$ .

A) $\frac{75}{(5 t+5)^{3}}$
B) $\frac{15}{(5 t+5)^{2}}$
C) $\frac{-15}{(5 t+5)^{2}}$
D) $\frac{-150}{(5 t+5)^{3}}$

Question 74

$\mathrm{s}$ is the distance (in $\mathrm{ft}$ ) traveled in time $\mathrm{t}$ (in s) by a particle. Find the velocity and acceleration at the given time.

- $s=\frac{1}{t+2}, t=5$

A) $v=-\frac{2}{343} \mathrm{ft} / \mathrm{s}, a=\frac{1}{49} \mathrm{ft} / \mathrm{s}^{2}$
B) $\mathrm{v}=\frac{2}{343} \mathrm{ft} / \mathrm{s}, \mathrm{a}=-\frac{1}{49} \mathrm{ft} / \mathrm{s}^{2}$
C) $v=\frac{1}{49} \mathrm{ft} / \mathrm{s}, \mathrm{a}=-\frac{2}{343} \mathrm{ft} / \mathrm{s}^{2}$
D) $v=-\frac{1}{49} \mathrm{ft} / \mathrm{s}, a=\frac{2}{343} \mathrm{ft} / \mathrm{s}^{2}$

Question 75

$\mathrm{s}$ is the distance (in $\mathrm{ft}$ ) traveled in time $\mathrm{t}$ (in s) by a particle. Find the velocity and acceleration at the given time.

- $s=2 t^{3}+7 t^{2}+7 t+9, t=2$

A) $v=40 \mathrm{ft} / \mathrm{s}, a=26 \mathrm{ft} / \mathrm{s}^{2}$
B) $v=38 \mathrm{ft} / \mathrm{s}, a=59 \mathrm{ft} / \mathrm{s}^{2}$
C) $v=26 \mathrm{ft} / \mathrm{s}, a=40 \mathrm{ft} / \mathrm{s}^{2}$
D) $v=59 \mathrm{ft} / \mathrm{s}, a=38 \mathrm{ft} / \mathrm{s}^{2}$

Question 76

$\mathrm{s}$ is the distance (in $\mathrm{ft}$ ) traveled in time $\mathrm{t}$ (in s) by a particle. Find the velocity and acceleration at the given time.

- $s=5 t^{3}+6 t^{2}+9 t+2, t=1$

A) $\mathrm{v}=36 \mathrm{ft} / \mathrm{s}, \mathrm{a}=42 \mathrm{ft} / \mathrm{s}^{2}$
B) $v=27 \mathrm{ft} / \mathrm{s}, a=3 \mathrm{ft} / \mathrm{s}^{2}$
C) $v=42 \mathrm{ft} / \mathrm{s}, a=36 \mathrm{ft} / \mathrm{s}^{2}$
D) $v=3 \mathrm{ft} / \mathrm{s}, a=27 \mathrm{ft} / \mathrm{s}^{2}$

Question 77

$\mathrm{s}$ is the distance (in $\mathrm{ft}$ ) traveled in time $\mathrm{t}$ (in s) by a particle. Find the velocity and acceleration at the given time.

- $s=-5 t^{3}+3 t^{2}-5 t-4, t=2$

A) $v=-8 \mathrm{ft} / \mathrm{s}, a=-53 \mathrm{ft} / \mathrm{s}^{2}$
B) $v=-53 \mathrm{ft} / \mathrm{s}, \mathrm{a}=-54 \mathrm{ft} / \mathrm{s}^{2}$
C) $v=-54 \mathrm{ft} / \mathrm{s}, a=-53 \mathrm{ft} / \mathrm{s}^{2}$
D) $v=-53 \mathrm{ft} / \mathrm{s}, a=-8 \mathrm{ft} / \mathrm{s}^{2}$

Question 78

$\mathrm{s}$ is the distance (in $\mathrm{ft}$ ) traveled in time $\mathrm{t}$ (in s) by a particle. Find the velocity and acceleration at the given time.

- $s=\sqrt{t^{2}-5}, t=3$

A) $\mathrm{v}=-\frac{5}{8} \mathrm{ft} / \mathrm{s}, \mathrm{a}=1.5 \mathrm{ft} / \mathrm{s}^{2}$
B) $\mathrm{v}=1.5 \mathrm{ft} / \mathrm{s}, \mathrm{a}=-\frac{5}{8} \mathrm{ft} / \mathrm{s}^{2}$
C) $\mathrm{v}=-1.5 \mathrm{ft} / \mathrm{s}, \mathrm{a}=\frac{5}{8} \mathrm{ft} / \mathrm{s}^{2}$
D) $\mathrm{v}=\frac{5}{8} \mathrm{ft} / \mathrm{s}, \mathrm{a}=-1.5 \mathrm{ft} / \mathrm{s}^{2}$

Question 79

Find the coordinates of the points of inflection for the function.

- $f(x)=x^{2}+6 x+11$

A) $(-4,1)$
B) $(-3,2)$
C) $(-2,3)$
D) There are no points of inflection.

Question 80

Find the coordinates of the points of inflection for the function.

- $f(x)=x^{3}+9 x^{2}+24 x+21$

A) $(-4,5)$
B) $(-2,1)$
C) $(-3,3)$
D) There are no points of inflection.