le (chl528) – HW04 – seckin – (57195)
1
This
print-out
should
have
19
questions.
Multiple-choice questions may continue on
the next column or page – find all choices
before answering.
001
10.0 points
Find the
x
-intercept of the tangent line at
the point
P
(
−
4
,
3) on the graph of
f
when
lim
h
→
0
f
(
−
4 +
h
)
−
3
h
= 5
.
1.
x
-intercept =
23
5
2.
x
-intercept =
−
23
3.
x
-intercept =
−
23
5
correct
4.
x
-intercept = 23
5.
x
-intercept =
−
17
5
6.
x
-intercept =
−
17
Explanation:
Since
lim
h
→
0
f
(
−
4 +
h
)
−
f
(
−
4)
h
is the slope of the tangent line at
P
(
−
4
,
3)
,
an equation for this tangent line is
y
−
3 = 5(
x
+ 4)
,
i.e.
,
y
= 5
x
+ 23
.
Consequently, the
x
-intercept =
−
23
5
.
002
10.0 points
Consider the slope of the given curve at the
five points shown.
C
E
A
B
D
List the five slopes in decreasing order.
1.
E, B, C, D, A
2.
E, C, A, D, B
3.
B, D, E, C, A
4.
D, C, E, A, B
5.
D, B, C, A, E
6.
B, D, A, C, E
correct
Explanation:
The order will be the one from most positive
slope to most negative slope. Inspection of the
graph shows that this is
B, D, A, C, E
.
003
10.0 points
Find an equation for the tangent line at the
point
P
(
−
2
,f
(
−
2)) on the graph of
f
when
f
is defined by
f
(
x
) = 3
x
2
+
x
+ 3
.
1.
y
+ 11
x
+ 9 = 0
correct
2.
y
−
11
x
+ 9 = 0
3.
y
−
11
x
−
9 = 0
4.
y
+ 11
x
+ 15 = 0