Answer Key Math 1142 Fall 2005 Final Exam
Answer Key Math 1142 Fall 2005 Final Exam
Answer Key Math 1142 Fall 2005 Final Exam
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<strong>Answer</strong> <strong>Key</strong><br />
<strong>Math</strong> <strong>1142</strong><br />
<strong>Fall</strong> <strong>2005</strong> <strong>Final</strong> <strong>Exam</strong><br />
Multiple Choice Problems<br />
1. B<br />
2. D<br />
3. A<br />
4. C<br />
5. D<br />
6. E<br />
7. B<br />
8. A<br />
9. E<br />
10. C<br />
11. E<br />
12. B<br />
13. C<br />
14. B<br />
Written <strong>Answer</strong> Problems<br />
15. on [ −1 , 3 ] -- f ( 3 ) =<br />
absolute minimum<br />
3<br />
3<br />
is the absolute maximum,<br />
f (−1) = − 1 2<br />
is the<br />
16.<br />
a) intervals € of increase: ( −∞ , −2 ) , ( 2 , ∞ ) , interval € of decrease: ( −2 , 2 )<br />
b) inflection point at ( 0, 3 ) ; interval of upward concavity: ( 0 , ∞ ) ,<br />
interval of downward concavity: ( −∞ , 0 )<br />
c) local maximum at ( −2, 19 ) , local minimum at ( 2, −13 )<br />
d) see graph below<br />
17. y = ½ ln ( x 2 – 6x + 4 )<br />
18.<br />
a)<br />
dy<br />
dx = 2e−x (4 + 14x − 3x 2 ) (3x + 4 ) 4 b)<br />
1<br />
4 x 2 ln x − 1 8 x 2 + C<br />
19. maximum volume is 256<br />
€ 20.<br />
2 ( ln [ 3 + 2 3 ] − ln [ 3 ] ) or ln (7 + 4€<br />
3 )<br />
€<br />
(continued)
graph for Problem #16(d) –
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