### Home > APCALC > Chapter 7 > Lesson 7.1.5 > Problem 7-50

Use the first and second derivatives to determine the following locations for . Homework Help ✎

Relative minima and maxima

Remember: Finding where

orDNE will identify CANDIDATES for minima and maxima.

You need to complete the 1st or 2nd Derivative Test to confirm which is which.Intervals over which

*f*is increasing and decreasingWhen

is positive, thenhas positive slopes, which meansis increasing.Inflection points

Remember: Finding where

or= DNE will identify CANDIDATES for inflection points.

You need to do further investigation to determine if it is (or is not) an inflection point.Either test for a sign change of

before and after the candidate point. Or evaluateat the candidate.

If≠ 0, then it is a point of inflection.Intervals over which

*f*is concave up and concave downWhen

is positive, thenhas positive slopes, which meansis concave up.