math

 For the function

sketched below, find for what

http://calculus.sfsu.edu/latexrender?src=%5Cbegin%7Bdisplaymath%7D+%5Ctextstyle%7Bx%7D+%5Cend%7Bdisplaymath%7D&type=png&size=15

does the function

(x)

reach

(a) the absolute maximum value,

(b) the absolute minimum value,

(c) What is the absolute maximum value of

?,

(d) What is the absolute minimum value of

?

 For the function

sketched above, find

(a) values

for which

'(c) = 0

,

(b) values

for which

'(c)

does not exist,

(c) values

at which

(x)

is not continuous?

(d) Does the function reach every value between its absolute minimum value and its absolute maximum value?

Problems 3--5. The following functions are defined for all

. Find the critical numbers if they exist. Explain in a sentance how you do it.



.





 Find critical numbers for

where

> 0

. What will you do first?

 Find the maximum and minimum values of

defined on the interval

3,6]

.

 Find the maximum and minimum values of

defined on the interval

-2,6]

.

 Find the maximum and minimum values of

on the interval

-pi/4, pi/2]

. Then graph the function to check your answers.

 Sketch the graph of

Does

http://calculus.sfsu.edu/latexrender?src=%5Cbegin%7Bdisplaymath%7D+%5Ctextstyle%7Bf%7D+%5Cend%7Bdisplaymath%7D&type=png&size=15

have an absolute maximum value? If so for what values of

http://calculus.sfsu.edu/latexrender?src=%5Cbegin%7Bdisplaymath%7D+%5Ctextstyle%7Bx%7D+%5Cend%7Bdisplaymath%7D&type=png&size=15

is this maximum achieved?