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

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? Homework Help ✎

Find the critical points by setting both *f* '(*x*) and *f* "(*x*) equal to zero and by finding where *f* '(*x*) does not exist.

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