Key to the Practice Final

Problem 1

A. [-6x² + 6x]/(1 - 2x)²

B.  5/2 x(5x²  + 9)^-1/2  

C.  -2/5

Problem 2

A.  3/4

B.  Does Not Exist

Problem 3

A.  -2, -.5, 1, 3

B.  -3, -2, -.5, 1, 3

Problem 4

Area is about (160,0000) square feet.

Error is about +-1600 pi = +- 5027 square feet.

Problem 5

$73 per ticket.

Problem 6

y' = 1 - 1/(x - 1)²

y'' = 2/(x - 1)³

y' = 0 when 1 - 1/(x - 1)² = 0 or (x - 1)² = 1 so that x = 2 or x = 0

y''(2) > 0 and y''(0) < 0 hence

(0,-1) is a local maximum and (2,3) is a local minimum.

Notice that y'' is never 0, hence there are no inflection points.  

There is a vertical asymptote at x = 1 and no horizontal asymptotes.

The function is increasing on (-infinity,0) and (2,infinity) and decreasing on (0,2).  

The function is concave down on (-infinity,1) and concave up on (1,infinity)