### Home > CALC > Chapter 7 > Lesson 7.3.3 > Problem7-138

7-138.

Find all relative maxima, minima, and points of inflection given $f(x) = 2x^{5/3}-5x^{4/3}$.

Candidates for relative maxima and minima occur where $f^\prime(x) = 0$ and $f^\prime(x) =$ DNE.
Candidates for points of inflection occur where $f^{\prime\prime}(x) = 0$ and $f^{\prime\prime}(x) =$ DNE.
But these are just CANDIDATES.
You have to conduct other tests before identifying each candidate as the location of a max, min or POI.

Once you determine the $x$-value of each relative max, relative min and POI, recall that maxima and minima are defined as $y$-values.
Use the function $f(x)$ to determine the corresponding $y$-coordinates.