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## Homework Statement

Suppose the graph f''(x) of a function is given by:

(see attachment)

(a) Find all points of inflection of f(x)

## The Attempt at a Solution

First I figured, by looking at the graph and seeing the intercept points [(-2,0),(0,0),(2,0)] that f''(x) = [tex]x^{4}-4x^{2}[/tex]

solving for f''(x)=0 gives us x = -2 or 0 or 2.

Between -2 < x < 2 there is no change of sign, which indicates no point of inflection.

Thus the points of inflection for f(x) are at x = -2 and x = 2.

correct?

But how can I find the y intercepts with just what I have? I only know how to find them by putting x back into f(x). As we don't have f(x) here, I'm stuck. Integrating back doesn't help because of the unknown variables.

Or am I trying too hard, and what I've done is the answer?