Math 1100
Homework 12
Name:
1. Let f (x) = x3 − 2x
(a) (4 points) Find f 0 (x).
(b) (4 points) Find f 00 (x).
(c) (4 points) Find all critical values of f .
(d) (4 points) On what intervals is f (x) concave up?
(e) (4 points) On what intervals is f (x) concave down?
30 September, 2013
(f) (4 points) Find all relative maximum points of f (x). Give the point, not just the
x-value. Justify your answer with reference to the second derivative and/or the
concavity of the function.
(g) (4 points) Find all relative minimum points of f (x). Give the point, not just the
x-value. Justify your answer with reference to the second derivative and/or the
concavity of the function.
(h) (4 points) Draw the graph of f (x) on the axes below.