### Home > CALC > Chapter 5 > Lesson 5.2.4 > Problem5-93

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?

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.