Home > CALC > Chapter 5 > Lesson 5.3.3 > Problem 5-132
For each part below, what can you conclude (if anything) about
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
, the nd 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 then is a POI, if not then it's not.
2. You could evaluate therd-derivative at . If it is NOT zero, then is 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
or does not exist.
Condition 2: Refer to hints in part (a) or part (b).does not exist and for and for . Refer to hint in part (e).