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

5-93.

Determine all critical points for the function $f\left(x\right) = x^{3} + x^{2/3}$. Which points are minima, maxima, and points of inflection? Homework Help ✎

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

$f'(x):3x^{2}+\frac{2}{3}x^{-\frac{1}{3}}$

$f''(x):6x-\frac{2}{9}x^{-\frac{4}{3}}$