Math 165
Fall 2002
a) b)
c) d)
e)
a)
Find
the derivative of the function.
b)
Find
all of the critical numbers of the function.
c)
Find
the maximum and minimum values of the function on [2,3].
4. (10 pt) I wish to paint a large hemispherical dome of radius 50 feet. If my coat of paint is to be 0.1 inches thick, use differentials to estimate the amount of paint that I will need (in either cubic feet or cubic inches).
a)
Show
that is a critical number
for if and only if is a critical number for
b)
Explain
why is a local maximum if
and only if is a local maximum.