Math 181

July 9, 2013

1. Find the critical numbers of the following functions:

So the critical numbers for f are 5 and -1.

So the critical numbers for g are 0, 6, and -2

*In class I solved this
by expanding h(x) first. Here is the
solution via the product rule:*

*So the critical
numbers are when x=2/5 (h’(x)=0 there) and when x=0
(h’(x) dne there)*

2) Use your graphing calculator to help you determine whether each critical point you found above is a relative maximum, relative minimum, or neither:

a)

*Use your calculator to check!*

b)

c)

3) Find the absolute maximum and absolute minimum values of the functions from #1 on the interval [-10,10]

a) *f*(x):

*For each function, check the value of the
function at the endpoints of the interval*

* (-10 and 10) as well as at the critical points found above. The greatest function value*

b) *g*(x): *that you
found will be the absolute maximum on this interval, and the smallest value*

*will be the absolute minimum.*

c) h(x):