Consider the function
f(x) = 1
12
x
3 − x − 1.
Answer the following questions and use your answers to sketch an accurate
graph of f(x). No need to use a calculator!
(a) Find f
0
(x).
(b) Find the critical points of f.
(c) Find the interval(s) on which f is increasing and the interval(s) on
which f is decreasing
(d) Find f
00(x).
(e) Find the interval(s) on which f is concave up and the interval(s) on
which f is concave down.
(f) Find any inflection points of f