In below Problems a function and its first and second derivatives are given. Use these to find any horizontal and vertical asymptotes, critical points, relative maxima, relative minima, and points of inflection. Then sketch the graph of each function.

1. y = x / (x -1)2

y' = - x+1 / (x-1)3

y'' = 2x + 4 / ( x-1)4

2. y = (x -1)2 / x2

y' = 2( x-1) / x3

y'' = 6 - 4x / x4

y' = 1 - 1/(x-3) 4/3
y''= 4/ 3(x-3)7/3
4. y = 3 3√x + 1/x
y' = x4/3-1 / x2
y'' = 6-2x 4/3 /3x3
5.f (x) = 9(x-2) 2/3 / x2
f ' (x) = 12(3 - x) / x3(x - 2) 1/3
f '' (x) = 4(7x2 - 42x + 54) / x4 ( x - 2) 4/3

3 + V 3 3