Question 1

Estimate the slope of the curve at the indicated point.&#10; &#10;A) -1&#10;B) 0&#10;C) Undefined&#10;D) 1

Accepted Answer

B

Question 2

Find an equation for the tangent to the curve at the given point.&#10;

Accepted Answer

First, we find the slope of the tangent line by taking the derivative of the curve:
$$y' = 2x - 1$$
Then, we evaluate it at the point (-4,20):
$$y' = 2(-4) - 1 = -9$$
So the slope of the tangent line is -9. Next, we use the point-slope formula to find the equation of the line:
$$y - y_1 = m(x - x_1)$$
Plugging in (-4,20) and -9 for m, we get:
$$y - 20 = -9(x + 4)$$
Simplifying gives:
$$y = -9x -16$$
So the equation of the tangent line is y = -9x -16, or choice C.

Question 3

Graph the equation and its tangent.&#10;

Accepted Answer

To find the equation of the tangent, we need to find the slope at the point $(-2,7)$. We can find the slope by taking the derivative of the function: $y'=2x-3$. Substituting $x=-2$ gives $y'=-7$.

So, the equation of the tangent at $(-2,7)$ is

$y = (-7)(x+2) + 7$

Simplifying, we get $y=-7x-7$

Graphing the equation of the curve and the tangent line in the same coordinate plane, we see that choice B is the correct answer.

Question 4

Find an equation for the tangent to the curve at the given point.&#10;

Accepted Answer

To find the slope of the tangent line, we take the derivative of the function: $y' = 2x$. Plugging in $x=-4$ (since we want the tangent at $(-4,14)$), we get $y'=-8$.

Now, we have the slope of the line and a point on the line. Using point-slope form, we get: $y-14 = -8(x+4)$. Simplifying, we get $y=-8x-18$. Therefore, the answer is choice C.

Question 5

Graph the equation and its tangent.&#10;

Accepted Answer

The answer of Graph the equation and its tangent.&#10; ...

Question 6

Estimate the slope of the curve at the indicated point.&#10;

Accepted Answer

The slope of the curve at a given point is equal to the derivative of the function at that point. From the graph, we can see that the tangent line at the indicated point has a negative slope. This means that the function is decreasing at that point. The only choice that represents a negative slope is C, $- \frac { 1 } { 2 }$.

Question 7

Find an equation for the tangent to the curve at the given point.&#10;

Accepted Answer

To find the equation of the tangent line, we first need to find the derivative of the function: 
$$f'(x) = \frac{5}{\sqrt{x}} - 1$$
Then evaluate the derivative at x=100 to find the slope of the tangent line:
$$f'(100) = \frac{5}{\sqrt{100}} - 1 = 1$$
So the slope of the tangent line is 1. Using the point-slope form of the equation of a line, we have:
$$y - 3 = 1(x-100)$$
Simplifying, we get:
$$y = -\frac{1}{2}x + 53$$
Therefore, the correct answer is D.

Question 8

Find an equation for the tangent to the curve at the given point.&#10;

Accepted Answer

To find the equation of the tangent line at a point, we first need the derivative of the given function to find the slope at that point. The derivative of $y = \frac{x^3}{2}$ is $y' = \frac{3x^2}{2}$. Plugging in the x-value of the point (6) into the derivative gives the slope at that point: $y' = \frac{3(6)^2}{2} = 54$. The equation of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. We have the slope (54) and a point (6, 108), so we can solve for $b$: $108 = 54(6) + b$, which simplifies to $b = -216$. Therefore, the equation of the tangent line is $y = 54x - 216$.

Question 9

Graph the equation and its tangent.&#10;

Accepted Answer

The answer of Graph the equation and its tangent.&#10; ...

Question 10

Estimate the slope of the curve at the indicated point.&#10; &#10;A) Undefined&#10;B) 1&#10;C) -1&#10;D) 0

Accepted Answer

The answer of Estimate the slope of the curve at...

Question 11

Estimate the slope of the curve at the indicated point.&#10; &#10;A) Undefined&#10;B) 1&#10;C) 0&#10;D) -1

Accepted Answer

The answer of Estimate the slope of the curve at...

Question 12

Estimate the slope of the curve at the indicated point.&#10; &#10;A) 1&#10;B) -1&#10;C) 0&#10;D) Undefined

Accepted Answer

The answer of Estimate the slope of the curve at...

Question 13

Find an equation for the tangent to the curve at the given point.&#10;

Accepted Answer

The answer of Find an equation for the tangent to...

Question 14

Find an equation for the tangent to the curve at the given point.&#10;

Accepted Answer

The answer of Find an equation for the tangent to...

Question 15

Graph the equation and its tangent.&#10;

Accepted Answer

The answer of Graph the equation and its tangent.&#10; ...

Question 16

Estimate the slope of the curve at the indicated point.&#10;

Accepted Answer

The answer of Estimate the slope of the curve at...

Question 17

Estimate the slope of the curve at the indicated point.&#10; &#10;A) Undefined&#10;B) 1&#10;C) 0&#10;D) -1

Accepted Answer

The answer of Estimate the slope of the curve at...

Question 18

Graph the equation and its tangent.&#10;

Accepted Answer

The answer of Graph the equation and its tangent.&#10; ...

Question 19

Estimate the slope of the curve at the indicated point.&#10;

Accepted Answer

The answer of Estimate the slope of the curve at...

Question 20

Find an equation for the tangent to the curve at the given point.&#10;

Accepted Answer

The answer of Find an equation for the tangent to...

Question 21

Solve the problem.&#10;

Accepted Answer

The answer of Solve the problem.&#10; ...

Question 22

Solve the problem.&#10; &#10;A) 41 mph&#10;B) 5 mph&#10;C) 10 mph&#10;D) 4 mph

Accepted Answer

The answer of Solve the problem.&#10; &#10;A) 41 mph&#10;B) 5...

Question 23

Solve the problem.&#10;A cubic salt crystal expands by accumulation on all sides. As it expands outward find the rate of change of its volume with respect to the length of an edge when the edge is 0.27 mm.

Accepted Answer

The answer of Solve the problem.&#10;A cubic salt crystal expands...

Question 24

Solve the problem.&#10;

Accepted Answer

The answer of Solve the problem.&#10; ...

Question 25

Provide an appropriate response.&#10;

Accepted Answer

The answer of Provide an appropriate response.&#10; ...

Question 26

Find the slope of the curve at the indicated point.&#10; &#10;A) m = 2&#10;B) m = 7&#10;C) m = 4&#10;D) m = 10

Accepted Answer

The answer of Find the slope of the curve at...

Question 27

Solve the problem.&#10; &#10;A) 10.6 W/mph&#10;B) 4.8 W/mph&#10;C) 32.8 W/mph&#10;D) 0.5 W/mph

Accepted Answer

The answer of Solve the problem.&#10; &#10;A) 10.6 W/mph&#10;B) 4.8...

Question 28

Solve the problem.&#10;

Accepted Answer

The answer of Solve the problem.&#10; ...

Question 29

Solve the problem.&#10;Find the points where the graph of the function have horizontal tangents.

Accepted Answer

The answer of Solve the problem.&#10;Find the points where the...

Question 30

Solve the problem.&#10;

Accepted Answer

The answer of Solve the problem.&#10; ...

Question 31

Solve the problem.&#10;

Accepted Answer

The answer of Solve the problem.&#10; ...

Question 32

Solve the problem.&#10;Find the points where the graph of the function have horizontal tangents.

Accepted Answer

The answer of Solve the problem.&#10;Find the points where the...

Question 33

Find the slope of the curve at the indicated point.&#10; &#10;A) m = -16&#10;B) m = -8&#10;C) m = 8&#10;D) m = 16

Accepted Answer

The answer of Find the slope of the curve at...

Question 34

Solve the problem.&#10;

Accepted Answer

The answer of Solve the problem.&#10; ...

Question 35

Solve the problem.&#10;

Accepted Answer

The answer of Solve the problem.&#10; ...

Question 36

Find the slope of the curve at the indicated point.&#10; &#10;A) m = -18&#10;B) m = -3&#10;C) m = -12&#10;D) m = 3

Accepted Answer

The answer of Find the slope of the curve at...

Question 37

Solve the problem.&#10;

Accepted Answer

The answer of Solve the problem.&#10; ...

Question 38

Provide an appropriate response.&#10;

Accepted Answer

The answer of Provide an appropriate response.&#10; ...

Question 39

Solve the problem.&#10;

Accepted Answer

The answer of Solve the problem.&#10; ...

Question 40

Find the slope of the curve at the indicated point.&#10;

Accepted Answer

The answer of Find the slope of the curve at...

Question 41

Find the indicated derivative.&#10;

Accepted Answer

The answer of Find the indicated derivative.&#10; ...

Question 42

Differentiate the function and find the slope of the tangent line at the given value of the independent variable.&#10; &#10;A) -31&#10;B) -1&#10;C) 1&#10;D) 31

Accepted Answer

The answer of Differentiate the function and find the slope...

Question 43

Find the indicated derivative.&#10;

Accepted Answer

The answer of Find the indicated derivative.&#10; ...

Question 44

Differentiate the function and find the slope of the tangent line at the given value of the independent variable.&#10;

Accepted Answer

The answer of Differentiate the function and find the slope...

Question 45

Differentiate the function and find the slope of the tangent line at the given value of the independent variable.&#10;

Accepted Answer

The answer of Differentiate the function and find the slope...

Question 46

Find an equation of the tangent line at the indicated point on the graph of the function.&#10;

Accepted Answer

The answer of Find an equation of the tangent line...

Question 47

Calculate the derivative of the function. Then find the value of the derivative as specified.&#10;

Accepted Answer

The answer of Calculate the derivative of the function. Then...

Question 48

Calculate the derivative of the function. Then find the value of the derivative as specified.&#10;

Accepted Answer

The answer of Calculate the derivative of the function. Then...

Question 49

Provide an appropriate response.&#10;

Accepted Answer

The answer of Provide an appropriate response.&#10; ...

Question 50

Calculate the derivative of the function. Then find the value of the derivative as specified.&#10;

Accepted Answer

The answer of Calculate the derivative of the function. Then...

Question 51

Provide an appropriate response.&#10;

Accepted Answer

The answer of Provide an appropriate response.&#10; ...

Question 52

Calculate the derivative of the function. Then find the value of the derivative as specified.&#10;

Accepted Answer

The answer of Calculate the derivative of the function. Then...

Question 53

Provide an appropriate response.&#10;

Accepted Answer

The answer of Provide an appropriate response.&#10; ...

Question 54

Find the indicated derivative.&#10;

Accepted Answer

The answer of Find the indicated derivative.&#10; ...

Question 55

Calculate the derivative of the function. Then find the value of the derivative as specified.&#10;

Accepted Answer

The answer of Calculate the derivative of the function. Then...

Question 56

Find the indicated derivative.&#10;

Accepted Answer

The answer of Find the indicated derivative.&#10; ...

Question 57

Calculate the derivative of the function. Then find the value of the derivative as specified.&#10;

Accepted Answer

The answer of Calculate the derivative of the function. Then...

Question 58

Calculate the derivative of the function. Then find the value of the derivative as specified.&#10;

Accepted Answer

The answer of Calculate the derivative of the function. Then...

Question 59

Calculate the derivative of the function. Then find the value of the derivative as specified.&#10;

Accepted Answer

The answer of Calculate the derivative of the function. Then...

Question 60

Calculate the derivative of the function. Then find the value of the derivative as specified.&#10;

Accepted Answer

The answer of Calculate the derivative of the function. Then...

Question 61

Given the graph of f, find any values of x at which f is not defined.&#10; &#10;A) x = -2, 0, 2&#10;B) x = 0&#10;C) x = 2&#10;D) x = -2, 2

Accepted Answer

The answer of Given the graph of f, find any...

Question 62

The graph of a function is given. Choose the answer that represents the graph of its derivative.&#10;

Accepted Answer

The answer of The graph of a function is given....

Question 63

11eb49f8_e026_d3bd_b71a_b7eb46f1d9c2_TB6591_0011eb49f8_e026_d3c1_b71a_03a0b94f011d_TB6591_00

Accepted Answer

The answer of 11eb49f8_e026_d3bd_b71a_b7eb46f1d9c2_TB6591_0011eb49f8_e026_d3c1_b71a_03a0b94f011d_TB6591_00...

Question 64

The graph of a function is given. Choose the answer that represents the graph of its derivative.&#10;

Accepted Answer

The answer of The graph of a function is given....

Deck 4: Derivatives