| 1.
so the sign study for f ' and behavior of f is"
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x<-3 |
x=-3 |
-3<x<1 |
x=1 |
x>1 |
| f ' |
positive |
zero |
negative |
zero |
positive |
| f |
increasing |
leveling off |
decreasing |
leveling off |
increasing |
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Answer C |
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| 2.
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Answer A |
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| 3.
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Answer D |
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| 4. 
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Answer A |
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| 5.
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Answer A |
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| 6. The graph of h' should have two locations indicating that
h has a slope of zero, one for a negative x value and one for a positive x
value. These should be the two zeros for h'. h' should be
positive, then zero, then negative, then zero, then positive. Two
graphs describe this: D and E. D is eliminated because the slope
is changing should not show any change in concavity. |
Answer E |
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| 7.
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Answer E |
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| 8. 
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Answer B |
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9. The total number of barrels of oil that passed
through the pipeline is 
or the area bounded by the function, t=0, t=24, and the t axis. This
approximately 600+600+600+600+600 or 3000 barrels. |
Answer D |
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| 10.
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Answer E |
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| 11.
Since f is a linear function, f ' (x) is a constant, and f "(x) is
zero.
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Answer A |
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| 12.
Therefore the limit from the left does not equal the limit from the
right, no limit exists at x=2. |
Answer E |
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| 13. f is not differentiable at x=0 because of the
discontinuity or x=2 because of the vertical tangent line. |
Answer B |
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| 14. 
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Answer E |
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| 15. 
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Answer B |
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| 16. 
The sign of f " changes sign only at x =1. |
Answer C |
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| 17. From the graph we know that f(1)=0, f '(1)>0, and
f "(1) <0 so the correct order is f "(1) < f(1) < f '(1) |
Answer D |
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| 18.
I.  each term
is getting larger so the series diverges.
II. This series converges.
III diverges since the series is harmonic |
Answer B |
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| 19. 
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Answer D |
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| 20.
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Ansser E |
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21.
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Answer C |
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22.
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Answer A |
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| 23. f is defined and continuous on the closed interval
[a,b]. f has a relative maximum at x=c for some point c in the
interval. We do not know if at (c,f(c)) is a differentiable or
non-differentiable point. So we do not know if I is true. But if
f '(c) exists it must be zero. If f '(c) exists, then the f "(c) must
be negative. II and III are true. |
Answer E |
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24. Since the slopes at the various points appear to be the
sum of the x and y values then
 . Also notice
when the x coordinate is one less than the y coordinate the slope is -1.
For A to be true at x=0 the slopes would equal 1. Not true
For B to be true when x<0 slopes would all be positive. Not true.
For D to be true as x is constant and y increases, the slope decreases.
Not true.
E is not true since the slopes do not follow the natural logarithm or
logarithmic curve. |
Answer C |
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| 25.
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Answer C |
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| 26.
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Answer E |
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| 27.
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Answer D |
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| 28. 
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Answer C |
