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

Question

Let f be a function defined on the closed interval -5<x<5 with f(1)=3. The graph of f', the derivative of f, consists of two semicircles and two segments

luigi0210 · Answer

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

luigi0210 · Answer

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jtvatsim · Answer

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

jtvatsim · Answer

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!

jtvatsim · Answer

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