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

7-138.

Find all relative maxima, minima, and points of inflection given *f*(*x*) = 2*x*^{5/3} − 5*x*^{4/3}. Homework Help ✎

Candidates for relative maxima and minima occur where *f*'(*x*) = 0 and *f* '(*x*) = DNE.

Candidates for points of inflection occur where *f* "(*x*) = 0 and *f* "(*x*) = DNE.

But these are just CANDIDATES.

You have to conduct other tests before indentifying 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.