Chapter 2.2, Problem 68E

For Exercises 67–73, assume that f is differentiable over $\left(-\infty ,\infty \right)$. Classify each of the following statements as either true or false. If a statement is false, explain why.

If $f$ has exactly two critical values at $x=a$ and $x=b$, where $a<b$, then there must exist at least one point of inflection at $x=c$ such that $a<c<b$. In other words, at least one point of inflection must exist between any two critical points.