calc 1 h/w

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3. Find the following given the two functions below.

$C:\Users\Stephanie\AppData\Local\Temp\geogebra.png$

a) : ___________________

b) : ___________________

c) : ___________________

4. Prove the quotient rule using the product rule and the chain rule.

5. The local linearization of at 3 is find if and

6. Let for all

a. For what values is ? b. List the intervals where is increasing.

Don’t use a graph.

c. List the intervals where is decreasing. d. Where does have a local maximum?

Don’t use a graph.

e. What is the local minimum value of ?

7. Consider the function g, whose graph is shown below. Use the graph to answer the questions that follow.

a. Find exact values for each of the following: b. Decide whether each of the following is True or False:

i. i.

ii. ii.

iii. iii.

iv. iv.

v. v.

′g 4( ) = ____________

()

=____________

′g 2( ) > ′g 7( )______________

()

______________

′g 7( ) = ____________

()

=____________

g 7( ) > ′g 7( )______________

()

______________

′g 3( ) = ____________

()

=____________

g 3( ) > ′g 4( )______________

()

______________

gg( )(6) = ____________

gg

()

(6)=____________

′g 2( ) > ′g 0( )______________

()

______________

′g 1( ) = ____________

()

=____________

′g −1( ) > g −1( )______________

g-1

()

>g-1

()

______________