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Math 131 Spring, 2004
Quiz 7(a)
Name:
Solutions
Without using a calculator. Show your work in detail. You may leave fractions or irrational numbers
in your answers.
U
1. (1pt) d fŸgŸx f ŸgŸx g U Ÿx dx
U
2. (10pts) Find f Ÿx where
1/3
a. fŸx 3 2x 3 " x Ÿ2x 3 " x U
f Ÿx 1 Ÿ2x 3 " x "2/3 Ÿ2Ÿ3x 2 " 1 1
3
3
b. fŸx ln
3
6x 2 " 1
2
Ÿ2x 3 " x secŸ2x e "3x
U
f Ÿx 2 secŸ2x tanŸ2x " 3e "3x
1
"3x
tanŸ2x Ÿ2 "
3e
ŸsecŸ2x secŸ2x e "3x
secŸ2x e "3x
c. fŸx cos 3 Ÿ x U
f Ÿx 3 cos 2 Ÿ x Ÿ" sinŸ x 1 x "1/2
2
" 3 sinŸ x cos 2 Ÿ x 2 x
2
3. (6pts) Find the equation of the tangent line to the curve y xe "x at the point where x 1. Find also all
values of x at which the tangent line is horizontal.
2
fŸx xe "x , fŸ1 Ÿ1 e "Ÿ1 1e
U
U
2
2
2
f Ÿx e "x x e "x Ÿ"2x e "x Ÿ1 " 2x 2 , m f Ÿ1 e "1 Ÿ1 " 2 " 1e
the equation of the tangent line: y " 1e " 1e Ÿx " 1 , y " 1e x 2e
U
2
Set f Ÿx 0, e "x Ÿ1 " 2x 2 0,
1
1 " 2x 2 0, x 2 1 , x o
2
1 o 1 .
2
2
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