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):