Rolle's Theorem

If a function satisfies 3 hypothesis:

1. $f$ is continuous on a closed interval $[a,b]$
2. $f$ is differentiable on a closed interval $(a,b)$
3. $f(a)=f(b)$ Then there is a number $c$ in $(a,b)$ such that $f^{\prime }(c)=0$ This means there must be atleast one point where the slope is 0

Proof

• Rolle’s Theorem Proof

Questions

• Prove function has exactly one real root