Question 1

Solve the problem.
-The percent of concentration of a certain drug in the bloodstream x hr after the drug is administered is given by  How long after the drug has been administered is the concentration a maximum? Round answer to the nearest tenth, if necessary.

Accepted Answer

The answer of Solve the problem.
-The percent of concentration of...

Question 2

Solve the problem.
-With x representing the water temperature in degrees Celsius,  approximation to the number of salmon swimming upstream to spawn. Find the temperature that produces the maximum number of salmon.

Accepted Answer

The answer of Solve the problem.
-With x representing the water...

Question 3

Find the intervals where f''(x) < 0 ir f''(x) > 0 as indicated.
-

Accepted Answer

The answer of Find the intervals where f''(x) < 0...

Question 4

Sketch a graph of the function.
-

Accepted Answer

The answer of Sketch a graph of the function.
-
...

Question 5

Find the intervals where the function has the indicated concavity. Give the x coordinates of inflection points.
-Concave upward

Accepted Answer

The answer of Find the intervals where the function has...

Question 6

Sketch a graph of the function.
-

Accepted Answer

The answer of Sketch a graph of the function.
-
...

Question 7

Find the intervals where the function has the indicated concavity. Give the x coordinates of inflection points.
-Concave downward

Accepted Answer

The answer of Find the intervals where the function has...

Question 8

Sketch a graph of a single function that has these properties.
-a) Continuous and differentiable for all real numbers
b)  
c)  
d)  
e)  
f)  
g) An inflection point at (0,0)

Accepted Answer

The answer of Sketch a graph of a single function...

Question 9

Sketch a graph of the function.
-

Accepted Answer

The answer of Sketch a graph of the function.
-
...

Question 10

Sketch a graph of the function.
-

Accepted Answer

The answer of Sketch a graph of the function.
-
...

Question 11

Sketch a graph of the function.
-

Accepted Answer

The answer of Sketch a graph of the function.
-
...

Question 12

Solve the problem.
-The cost of manufacturing x electric woks in one day is given by C(x) = 2x3 -16x2 + 4x. Find the average cost per electric wok and the interval where the average cost per electric wok is decreasing.

Accepted Answer

The answer of Solve the problem.
-The cost of manufacturing x...

Question 13

Sketch a graph of a single function that has these properties.
-Find

Accepted Answer

A function with a vertical asymptote at x=3 means the function approaches positive or negative infinity as x approaches 3 from either side. A function with a hole at x=2 means there is a point at (2,3) that is missing from the graph. We can create such a function by taking a rational function with a vertical asymptote at x=3 and cancelling out the common factor in the numerator and denominator at x=2 to create a hole. One possible function that satisfies these conditions is:

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

This function has a vertical asymptote at x=3 and a hole at x=2.

Question 14

Find the intervals where f''(x) < 0 ir f''(x) > 0 as indicated.
-

Accepted Answer

To find where f''(x) < 0, we need to look for where the function is concave down. This occurs when the second derivative is negative. From the graph, we can see that f''(x) is negative on the interval (-1, 1). Therefore, answer choices A, B, and D are incorrect. To find where f''(x) > 0, we need to look for where the function is concave up. This occurs when the second derivative is positive. From the graph, we can see that f''(x) is positive on the intervals (-∞, -1) and (1, ∞). Therefore, answer choice C is the best choice since it correctly identifies where f''(x) < 0 and f''(x) > 0.

Question 15

Solve the problem.
-The annual revenue and cost functions for a manufacturer of grandfather clocks are approximately  where x denotes the number of clocks made. What is the maximum annual profit?

Accepted Answer

The answer of Solve the problem.
-The annual revenue and cost...

Question 16

Sketch a graph of a single function that has these properties.
-a) Continuous and differentiable for all real numbers
b)  
c)  ) and ( -1 , 2)
d)  
e)  
f)  
g)

Accepted Answer

The answer of Sketch a graph of a single function...

Question 17

Find the intervals where f''(x) < 0 ir f''(x) > 0 as indicated.
-

Accepted Answer

The answer of Find the intervals where f''(x) < 0...

Question 18

Find the intervals where the function has the indicated concavity. Give the x coordinates of inflection points.
-Concave downward

Accepted Answer

The answer of Find the intervals where the function has...

Question 19

Solve the problem.
-The Olympic flame at the 1992 Summer Olympics was lit by a flaming arrow. As the arrow moved d feet horizontally from the archer, assume that its height h(d), in feet, was approximated by the function  Find the relative maximum of the function.

Accepted Answer

To find the relative maximum, we need to take the first derivative of the function and set it equal to zero. Then, we solve for d to find the x-coordinate of the relative maximum, and plug that value back into the original function to find the corresponding y-coordinate (height).

Taking the first derivative of h(d), we get:
h'(d) = (1/50)e^(3d/700) - (3/700)e^(3d/700)

Setting h'(d) equal to zero, we can solve for d:
(1/50)e^(3d/700) - (3/700)e^(3d/700) = 0
e^(3d/700) = 3/50
d = (700/3)ln(3/50) = 175

So, the x-coordinate of the relative maximum is d = 175. To find the corresponding y-coordinate (height), we plug d into the original function:

h(175) = 61.25

Therefore, the relative maximum is at (175, 68.15) and the best choice is D.

Question 20

Find the intervals where the function has the indicated concavity. Give the x coordinates of inflection points.
-Concave upward

Accepted Answer

The answer of Find the intervals where the function has...

Quiz 4: Graphing and Optimization

Solve the problem. -The percent of concentration of a certain drug in the bloodstream x hr after the drug is administered is given by How long after the drug has been administered is the concentration a maximum? Round answer to the nearest tenth, if necessary.

Solve the problem. -With x representing the water temperature in degrees Celsius, approximation to the number of salmon swimming upstream to spawn. Find the temperature that produces the maximum number of salmon.

Find the intervals where f''(x) < 0 ir f''(x) > 0 as indicated. -

Sketch a graph of the function. -

Find the intervals where the function has the indicated concavity. Give the x coordinates of inflection points. -Concave upward

Sketch a graph of the function. -

Find the intervals where the function has the indicated concavity. Give the x coordinates of inflection points. -Concave downward

Sketch a graph of a single function that has these properties. -a) Continuous and differentiable for all real numbers b) c) d) e) f) g) An inflection point at (0,0)

Sketch a graph of the function. -

Sketch a graph of the function. -

Sketch a graph of the function. -

Solve the problem. -The cost of manufacturing x electric woks in one day is given by C(x) = 2x3 -16x2 + 4x. Find the average cost per electric wok and the interval where the average cost per electric wok is decreasing.

Sketch a graph of a single function that has these properties. -Find

Find the intervals where f''(x) < 0 ir f''(x) > 0 as indicated. -

Solve the problem. -The annual revenue and cost functions for a manufacturer of grandfather clocks are approximately where x denotes the number of clocks made. What is the maximum annual profit?

Sketch a graph of a single function that has these properties. -a) Continuous and differentiable for all real numbers b) c) ) and ( -1 , 2) d) e) f) g)

Find the intervals where f''(x) < 0 ir f''(x) > 0 as indicated. -

Find the intervals where the function has the indicated concavity. Give the x coordinates of inflection points. -Concave downward

Solve the problem. -The Olympic flame at the 1992 Summer Olympics was lit by a flaming arrow. As the arrow moved d feet horizontally from the archer, assume that its height h(d) , in feet, was approximated by the function Find the relative maximum of the function.

Find the intervals where the function has the indicated concavity. Give the x coordinates of inflection points. -Concave upward