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151 WebCalc Fall 2002-copyright Joe Kahlig
Quiz #5
MATH 151 Section
Name:
September 19, 2002
1. Use these figures to answer these questions. Give exact answers if possible, otherwise approximate.
5
f(x)
4
3
5
2
4
3
1
2
g(x
1
−3
−3
−2
−1
1
2
3
4
5
6
−2
−1
1
2
3
4
5
6
−1
−1
−2
−2
(a) Determine the slope of the tangent line for g(x) at x = 5.
this answer depends on how you draw the tangent line and which points you pick from the
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graph. My tangent line is drawn on the figure. The approximate slope is 1.75
≈ 1.7142
(b) Find the average rate of change from x = 0 to x = 4 for g(x).
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The points are (0, 0) and (4, 2). answer: 2−0
4−2 = 2
(c) Find f 0 (4) = 23 .
2. Write down the difference quotient and then simplify it. The function is J(x) = 1 − 3x2 and
a = −1
J(−1 + h) − J(−1)
(1 − 3(−1 + h)2 ) − (−2)
1 − 3(1 − 2h + h2 ) + 2
=
=
=
h
h
h
1 − 3 − 6h − 3h2 + 2
6h − 3h2
=
= 6 − 3h
h
h