CPM Homework Help : CALC Problem 5-93

Suppose you are given a function $f(x) = x^3 + x^{2/3}$ . Determine all critical points. Which points are minimums, maximums, and points of inflection?

Hint 1:

Find the critical points by setting both $f^\prime(x)$ and $f^{\prime\prime}(x)$ equal to zero and by finding where $f^\prime(x)$ does not exist.

Hint 2:

Use your calculator to help you find the exact coordinates of all of the critical points.