EXAM 2 Section
October 12, 2006
NAME:
Note that to receive full credit on the short answer questions, relevant work and a correct answer must be
shown. An incorrect answer with correct work for the problem shown can receive partial credit. A correct
answer with no work shown can receive no credit.
Good luck!!
“On my honor, as a University of Colorado at Boulder student, I have neither given nor received unautho
rized assistance on this work.”
YOUR SIGNATURE:
1.
Tangent Line
(6 points) Find an equation of the tangent line to the curve
f
(
x
) =
−
5
3
x
2
+ 2
x
+ 2 at
x
=
−
1
.
Solution:
The slope of
f
(
x
) is given by the derivative:
f
′
(
x
) =
−
10
3
x
+ 2. So the slope of our desired
tangent line is
f
′
(
−
1) =
−
10
3
(
−
1)+2 =
16
3
.
Now
f
(
−
1) =
−
5
3
(
−
1)
2
+2(
−
1)+2 =
−
5
3
, so an equation
of the desired tangent line is:
y
=
16
3
x
+
11
3
.
1
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document2.
Derivatives
(4 points each) Find the derivative of the function. You DO NOT need to SIMPLIFY
your answer.
(a)
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '08
 JOHANSON
 Calculus, Derivative, Boulder, University of Colorado

Click to edit the document details