Answer Key
Topics Covered in the Exam:
•
Chapter 6: Section 19
Instructions:
•
There are 8 questions and 100 points total.
•
In order to get full credit, you should show all your work instead of putting down the
answers.
Please make your final answer clear by writing legibly and placing a box
around it.
•
If you are unable to do a problem, you can get partial credit for explaining where you got
stuck – doing so will help us to better understand what you know.
•
You have 50 minutes to complete the exam.
Good Luck.
Question 1
(10 points)
Let
2
( )
1
f x
x
x
=
 +
.
(a) (5 points) Compute the Newton quotient,
(
)
( )
f x
h
f x
h
+

Answer
2
2
(
)
( )
[(
)
(
) 1] (
1)
(2
1)
2
1
f x h
f x
x h
x h
x
x
h x h
x h
h
h
h
+

+

+
+

 +
+ 
=
=
=
+ 
(b) (3 points)
Write down the definition of
'( )
f x
and find
'( )
f x
by definition.
Answer
0
0
(
)
( )
'( )
lim
lim(2
1)
2
0 1
2
1
h
h
f x
h
f x
f x
x
h
x
x
h
x
+

=
=
+

=
+  =

(c) (2 points)
Give one interpretation for
'( )
f x
.
Answer
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 Fall '07
 ZHANG,TIAN
 Economics, Derivative, Monotonic function, Convex function

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