Key to Practice Midterm III

Problem 1.  

I.  A)  No relative extrema.

B)  Increasing on {x|x not -1}

C)  No points of inflection

D)  concave up for x < -1 and concave down for x > -1

II.  A)  relative max at x = 1, relative minimum at x = -1.

B)  Increasing for -1 < x < 1 and decreasing for x < -1 and for x > 1

C)  inflection points at 0, -sqrt3 and sqrt3

D)  concave up for -sqrt3 < x < 0 and sqrt3 < x < infinity

convave down for -infinity < x < -sqrt3 and 0 < x < sqrt3

III.  A)  Relative Max at x = 0, Relative Min at x = +-2

B)  Increasing for -2 < x < 0 and x > 2

Decreasing for x < -2 and 0 < x < 2

C)  Inflection points at +- 2/sqrt3

D)  Concave up for -infinity < x < -2/sqrt3 and 2/sqrt3 < x < infinity

concave down for -2/sqrt3 < x < 2/sqrt3

IV.  A)  Relative Min at x = 3/4

B)  Increasing for 3/4 < x < infinity

Decreasing for x < 3/4 except at x = 0

C)  Inflection point at 0 and 1/2

D)  concave up for -infinity < x < 0 and 1/2 < x < infinity

Concave down for 0 < x < 1/2

Problem 2

A.  R(x) = 5x - 0.05x²

B.  50

Problem 3 

30 by 60