Find the inflection points in the graph

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The question is which of the $x$-values of the given points are inflection points of the function $f(x)$ itself?

I chose $C,F$ and $H$ because at this point the $f'(x)$ is zero. But my answer was wrong. Why ? is it only $C$ & $F$ ?

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2 Answers

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Inflection points are points where the first derivative changes from increasing to decreasing or vice versa. Equivalently we can view them as local minimums/maximums of $f'(x)$.

Wiki page of Inflection Points:

From the graph we can then see that the inflection points are $B,E,G,H$.

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inflection point is where second derivatives are zero,so you may review to check where is second derivative zero

inflection points

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