This preview shows pages 1–2. Sign up to view the full content.
Math 1A, Spring 2008, Wilkening
Sample Midterm 2
You are allowed one 8
.
5
×
11 sheet of notes with writing on both sides. This sheet
must be turned in with your exam.
Calculators are not allowed.
1. (1 point) write your name, section number, and GSI’s name on your exam and
write your name on your sheet of notes.
2. (4 points) Find the equation of the tangent line to the curve
y
2
=
x
3
+ 3
x
2
at the
point (1
,

2).
Answer:
d
dx
(
y
2
) =
d
dx
(
x
3
+ 3
x
2
)
2
y
dy
dx
= 3
x
2
+ 6
x
2(

2)
dy
dx
= 3(1)
2
+ 6(1) = 9
dy
dx
=

9
4
so the equation of the tangent line is
y
+ 2 =

9
4
(
x

1).
3. (5 points) Find the relative maxima, minima and inﬂection points of the function
f
(
x
) =
xe

x
2
/
2
Answer:
f
0
(
x
) =
x
(

x
)
e

x
2
/
2
+
e

x
2
/
2
= (1

x
2
)
e

x
2
/
2
f
0
(
x
) = 0 if
x
=
±
1.
(because (1

x
2
) = 0 if
x
=
±
1)
f
0
(
x
)
>
0 if

1
< x <
1.
(because (1

x
2
)
>
0 if

1
< x <
1.)
f
0
(
x
)
<
0 if
x <

1 or
x >
1.
(because (1

x
2
)
<
0 if
x <

1 or
x >
1.)
(note:
e

x
2
/
2
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview. Sign up
to
access the rest of the document.
 Spring '08
 WILKENING
 Math, Calculus

Click to edit the document details