### Home > CALC > Chapter 7 > Lesson 7.1.5 > Problem 7-53

Use the first and second derivatives to determine the following locations for * *.

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 at which

is increasing and decreasing.When

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

Remember: Finding where

orDNE 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(candidate), then it is a point of inflection. Intervals at which

is concave up and concave down.When

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