Problem

The function

f(x) = x^{1/3}(x-1)

a. has 2 inflection points b. is strictly increasing for

x > \frac{1}{4}

and strictly decreasing for

x < \frac{1}{4}

c. is concave down in

\left( -\frac{1}{2}, 0 \right)

d. area enclosed by the curve lying in the fourth quadrant is

\frac{9}{28}