CPM Homework Help : CALC3RD Problem 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?

Hint:

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.

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

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

Hint:

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