| 76.
A is not true because the limit approaching a does not equal the function
value at a.
B is not true because f(a) is not the lowest value of the function
in a neighborhood around a.
C x=a is in the domain of f since there is a value for f(a).
D is true since limit as you approach a from the right and as you
approach a from the left is the same.
E is true. Since D is true then E would be true too. |
Answer A |
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| 77. Graphing the derivative of each
function we can then find the value of x that gives the same slope.
x=-3906 |
Answer C |
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| 78.
 |
Answer B |
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| 79. Graph f ' changes from positive to negative
therefore the function f is increasing and then decreasing. Therefore
a relative maximum occurs at the location of this change. The other
two graphs do not have this quality. |
Answer A |
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80.
Based on the graph of f ':
There are three critical values for f in the interval (0,10) |
Answer B |
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| 81.The absolute value function is continuous at
x=0 since the limit of the function equals 0 as you approach x=0 from the
left and the right. The absolute value function is not differentiable at
x=0 since the limit on the slope as you approach x=0 from the left is -1 and
from the right is +1.
The absolute value function has a absolute minimum at x=0. All
other function values in the domain are larger than 0. |
Answer D |
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| 82 . |
Answer E |
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83.
 |
Answer B |
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| 84.
 |
Answer A |
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| 85.
 |
Answer C |
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86.Using the function x+2y=8 and solving for y:
 This is the diameter
of the semicircle, so the radius is
 |
Answer C |
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| 87.
Solving for the zero:
Therefore the place where the slope is 1 is at x=.2367329.
The tangent line then is y=1(x-.2367329)+.1152256 or y=x-0.122 |
Answer D |
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| 88.
The final step is calculated in the calculator:
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89.
We know that g(x) < 0 so the sign of f ' can be determined by studying the
other factor
This factor is positive when x> 2 or x<-2 and negative between x=-2 and
x=2.
The sign study for f ' is
| x<-2 |
x=-2 |
-2<x<2 |
x=2 |
x>2 |
| negative |
0 |
positive |
0 |
negative |
Therefore f is described as follows:
| x<-2 |
x=-2 |
-2<x<2 |
x=2 |
x>2 |
| decreasing |
leveling off |
increasing |
leveling off |
decreasing |
There is a relative minimum at x = -2 and a relative maximum at x = 2 |
Answer B |
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| 90.
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Answer D |
