Stewart – Calculus ET 8e Chapter 14 Form F
____ 13. Suppose that over a certain region of space the electrical potential V is given by
.
Find the rate of change of the potential at in the direction of the vector .
Select the correct answer.
a.
b.
c. 44
d. 20
e. –0.96
14. Find the gradient of the function .
____ 15. If use the gradient vector to find the tangent line to the level curve
at the point .
Select the correct answer.
a.
b.
c.
d.
e.
16. Find and classify the relative extrema and saddle points of the function
for and .
17. Find the absolute extrema of the function
on the closed triangular region with vertices , and .
Stewart – Calculus ET 8e Chapter 14 Form F
____ 18. Suppose (1, 1) is a critical point of a function f with continuous second derivatives.
In the case of , , what can you say about f ?
Select the correct answer.
a. f has a local maximum at (1,1)
b. f has a saddle point at (1,1)
c. f has a local minimum at (1,1)
19. Find the points on the surface that are closest to the origin.
20. Find the dimensions of a rectangular box of maximum volume such that the sum of the lengths of its
12 edges is .
Stewart – Calculus ET 8e Chapter 14 Form F
Answer Key
Stewart – Calculus ET 8e Chapter 14 Form G
____ 1.
A contour map for a function f is shown. Use it to estimate the value of .
Select the correct answer.
a.
b. 78
c. 35
d. 28
e. 48
2. Find the domain and range of the function .
3. Find the domain and range of the function .
____ 4. Let Find
Select the correct answer.
a. 24
b.
3
2
c.
d.
6
Stewart – Calculus ET 8e Chapter 14 Form G
5. Determine the largest set on which the function is continuous.
6. Find the limit
____ 7. Find the limit Hint: If and then if
and only if
Select the correct answer.
a.
1
b.
0
c.
7
6
d.
6
7
8. How many nth-order partial derivatives does a function of two variables have?
____ 9. Use the definition of partial derivatives as limits to find if .
Select the correct answer.
a.
b.
c.
d.
e.
10. Find the indicated partial derivative.
Stewart – Calculus ET 8e Chapter 14 Form G
11. Use implicit differentiation to find
____ 12. Find the equation of the tangent plane to the given surface at the specified point. \
Select the correct answer.
a.
b.
c.
d.
e.
____ 13. A boundary stripe 2 in. wide is painted around a rectangle whose dimensions are 100 ft by 240 ft.
Use differentials to approximate the number of square feet of paint in the stripe.
Select the correct answer.
a. 113
b. 113.81
c. 113.22
d. 113.89
e. 113.33
14. Find the equation of the normal line to the given surface at the specified point.
Stewart – Calculus ET 8e Chapter 14 Form G
____ 15. Suppose that over a certain region of space the electrical potential V is given by
.
Find the rate of change of the potential at in the direction of the vector .
Select the correct answer.
a. 44
b.
c. 20
d.
e. –0.96
16. Find and classify the relative extrema and saddle points of the function
for and .
17. At what point is the following function a local maximum?
____ 18. Find the absolute minimum value of the function
on the set D. D is the region bounded by the parabola and the line
Select the correct answer.
a.
b.
c. 30
d.
e. 0
19. Find the dimensions of a rectangular box of maximum volume such that the sum of the lengths of its
12 edges is .
Stewart – Calculus ET 8e Chapter 14 Form G
____ 20. Find the shortest distance from the point to the plane .
Select the correct answer.
a.
b.
c.
d.
e.
Stewart – Calculus ET 8e Chapter 14 Form G
Stewart – Calculus 8e Chapter 14 Form G
Answer Section
Stewart – Calculus ET 8e Chapter 14 Form H
1. Find the domain and range of the function .
2. Find the domain and range of the function .
____ 3. Find for .
Select the correct answer.
a.
b.
c.
d.
e. 0
4. Find the indicated partial derivative.
5. Use implicit differentiation to find
6. Use implicit differentiation to find
Stewart – Calculus ET 8e Chapter 14 Form H
____ 7. Find for the function
Select the correct answer.
a.
b.
c.
d.
____ 8. Find the differential of the function
Select the correct answer.
a.
b.
c.
d.
9. Use the Chain Rule to find
____ 10. Find the directional derivative of at the point (1, 3) in the direction toward the
point (3, 1).
Select the correct answer.
a.
b.
c.
d. 28
e. none of these
11. Find the equation of the normal line to the given surface at the specified point.
Stewart – Calculus ET 8e Chapter 14 Form H
____ 12. Find the directional derivative of the function at the point in the
direction of the unit vector that makes the angle with the positive x-axis.
Select the correct answer.
a.
b. 13
c. 1
d.
13. Find the gradient of the function .
14. Find the maximum rate of change of at the point .
In what direction does it occur?
15. If use the gradient vector to find the tangent line to the level curve
at the point .
____ 16. At what point is the following function a local minimum?
Select the correct answer.
a.
b.
c.
d.
e.
17. At what point is the following function a local maximum?
Stewart – Calculus ET 8e Chapter 14 Form H
____ 18. Find the points on the surface that are closest to the origin.
Select the correct answer.
a.
b.
c.
d.
e.
19. Find the dimensions of the rectangular box with largest volume if the total surface area is given as
.
____ 20. Find the shortest distance from the point to the plane .
Select the correct answer.
a.
b.
c.
d.
e.
Stewart – Calculus ET 8e Chapter 14 Form H
Answer Key