Calculus I · Derivative applications, optimization, and related rates
Force two critical points from three roots
Problem
A differentiable function $f$ has $f(0)=f(2)=f(5)=0$. Prove that there are distinct numbers $c_1\in(0,2)$ and $c_2\in(2,5)$ with $f'(c_1)=f'(c_2)=0$.
Hint
There are two closed intervals with equal endpoint values.
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