Question

Let f be a function defined on the closed interval -5 13 years ago

Answer 1

for -5<x<5, find all values of x at which the graph of f has a point of inflection. justify your answer.

Answer 2

There will be points of inflection whenever the slope of y' is 0. That is when y'' = 0.

Answer 3

So, we need only identify the points on the graph of y' which you gave, where the slope is 0.
Watch out for "pointy" areas, the slope is undefined there!

Answer 4

So, the only points on the graph where it is flat (the slope is 0) are at x = -4 and x = -1.