### Home > APCALC > 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? (Note: Each part is different function.)

andThis is a justification about whether

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

forand This is a justification about whether

has a local max or a local min at. But which one?1st Derivative Test.

Complete the sentence: At

, the 2nd derivative is positive sois ____________________________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 the 2nd-derivative to the left of. If it changes signs thenis a POI, if not then it's not.

2. You could evaluate the 3rd-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. *f*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?*f*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 andforandforRefer to hint in part (e).