Larson_Calculus_10e ch13sec03
MULTIPLE CHOICE
1. Find the partial derivative for the function .
a.
b.
c.
d.
e.
2. Find the partial derivative for the function .
a.
b.
c.
d.
e.
3. Find the partial derivative for the function .
a.
b.
c.
d.
e.
4. Find the partial derivative for the function .
a.
b.
c.
d.
e.
5.
Find the partial derivative for the function .
a.
b.
c.
d.
e.
6. Find the partial derivative for the function .
a.
b.
c.
d.
e.
7. Find the partial derivative for the function .
a.
b.
c.
d.
e.
8. Find the partial derivative for the function .
a.
b.
c.
d.
e.
9. For , evaluate at the point .
a.
b.
c.
d.
e.
10. For , evaluate at the point .
a.
b.
c.
d.
e.
11. For , evaluate at the point .
a.
b.
c.
d.
e.
12. For , evaluate at the point .
a.
b.
c.
d.
e.
13. Find the first partial derivative for the function with respect to z.
a.
b.
c.
d.
e.
14. For , evaluate at the point .
a.
b.
c.
d.
e.
15. Find the second partial derivative for the function with respect to x.
a.
b.
c.
d.
e.
16. For find all values of x and y such that and
simultaneously.
a.
b.
c.
d.
e.
17. For find all values of x and y such that and
simultaneously.
a.
b.
c.
d.
e.
18. For , find all values of x and y such that and simultaneously.
a.
b.
c.
d.
e.
19. Suppose a pharmaceutical corporation has two plants that produce the same over-the-counter
medicine. If and are the numbers of units produced at plant 1 and plant 2, respectively, then
the total revenue for the product is given by . When
and find the marginal revenue for plant 1.
a.
174
b.
172
c.
80
d.
124
e.
93
20. Suppose a company manufactures two types of wood-burning stoves: a freestanding model and a
fireplace-insert model. The cost function for producing x freestanding and y fireplace-insert stoves is
. Find the marginal costs when and . Round your
answer to the nearest integer.
a.
192
b.
234
c.
210
d.
402
e.
403
21. Suppose the temperature at any point in a steel plate is where x and y
are measured in meters. At the point find the rate of change of the temperature with respect to
the distance moved along the plate in the direction of the x-axis. Round your answer to one decimal
place.
a.
b.
c.
d.
e.
22. Suppose the utility function is a measure of the utility (or satisfaction) derived by a person
from the consumption of two products x and y. Determine the marginal utility of product x if the utility
function is .
a.
b.
c.
d.
e.
23. Suppose the utility function is a measure of the utility (or satisfaction) derived by a person
from the consumption of two products x and y. Determine the marginal utility of product if the
utility function is .
a.
b.
c.
d.
e.