### Home > APCALC > Chapter 5 > Lesson 5.4.1 > Problem 5-144

5-144.

Determine the coordinates of all of the relative extrema and points of inflection for the function^{ }.^{ } Homework Help ✎

Max, min, and points of inflection on *f*(*x*) will occur where *f* '(*x*) = 0 or DNE or *f* ''(*x*) = 0 or DNE. But that alone is not enough to determine which is which.

Minima on *f*(*x*) happen where *f* '(*x*) changes from negative to positive.

Maxima on *f*(*x*) happen where *f* '(*x*) changes from positive to negative.

Inflection points on *f*(*x*) happen where *f* ''(*x*) changes sign.

Another way to distinguish between maxima and minima is to use the 2nd Derivative Test.