### Home > CALC > Chapter 5 > Lesson 5.3.3 > Problem 5-132

For each part below, what can you conclude (if anything) about if you know the given information below? (Note: Each part is separate.)

and.This is a justification about whether

has a local max or a local min at. But which one?2nd Derivative Test.

when,when, and.This is a justification about whether

has a local max or a local min at. But which one?st Derivative Test. Complete the sentence: At

, thend derivative is positive so is ____________________________Two words.

Refer to hint in part (c).

There might be a point of inflection on

at. But we do not know for sure. There are two ways to find out:

1. You could check thend-derivative to the left of . If it changes signs thenis a POI, if not then it's not.

2. You could evaluate therd-derivative at . If it is NOT zero, thenis a POI. If is is zero, then this method is inconclusive.

Since we are not given any extra information, we can only say thatis a CANDIDATE for a point of inflection. is continuous at, but not differentiable there.Examples of points of NON-differentiability include: cusps, endpoints, jumps, holes and vertical tangents.

Which of the above attributes still possess continuity?is defined and continuous everywhere, and has just one critical point at, which is a local maximum.Condition 1: Either

ordoes not exist.

Condition 2: Refer to hints in part (a) or part (b).does not exist andforandfor.Refer to hint in part (e).