APFIVE Inflection Points of an Even Function
Let $$f$$ be a function that is twice differentiable on $$-2 < x < 2$$ and satisfies the conditions in the table above. If $$f(x) = f(-x)$$, what are the $$x$$-coordinates of the points of inflection of the graph of $$f$$ on $$-2 < x < 2$$?
| $$0 < x < 1$$ | $$1 < x < 2$$ | |
|---|---|---|
| $$f(x)$$ | Positive | Negative |
| $$f'(x)$$ | Negative | Negative |
| $$f''(x)$$ | Negative | Positive |
A
There are no points of inflection on $$-2 < x < 2$$.
B
$$x = 0$$ only
C
$$x = -1$$ and $$x = 1$$
D
$$x = 1$$ only
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