Answer
TRUE
Work Step by Step
If a function is differentiable, then it is continuous. If $f(-1)=f(1)$ then there must either be a local or global maximum or minimum between -1 and 1 or $|c|\lt1$.
Thus, at some number between -1 and 1 there must be a number at which the derivative of the function at that point is zero.
Hence, the given statement is true.
