MATH 260
EXAM 2
1.
Find the indicated
derivatives for the following function:
a)
b)
2.
Does the following
limit exist:
3.
Find all local maximum
and minimum values of the function:
(Classify as maximum or minimum and justify).
Find the absolute maximum and minimum values of this function along the
rectangle bounded by the lines 
.
4.
You are given the task
of constructing a rectangular box that is to be of volume 32m3 with
no lid. Find the dimensions of the box that minimize the amount of material
(surface area) to be used.
5.
If you are given the
function of three variables 
with 
and 
. Use the chain rule to write 
.
6.
(Extra Credit 10pt) If
is a function of n variables, show that the direction of
greatest increase of the function at a point is in the direction of the
gradient (and that increase is equal to 
).