For each part below, what can you conclude (if anything) about f if you know the given information? (Note: Each part is different function.) Homework Help ✎
This is a justification about whether f(x) has a local max or a local min at
. But which one?
2nd Derivative Test.
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 so is ____________________________
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 then is a POI, if not then it's not.
2. You could evaluate the 3rd-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 that
is 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
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).