Question

what is Rolle's theorem?

Answer 1

If a function f(x)
* continuous in [a,b]
* differenciable in (a,b)
* f(a)=f(b)

then there exists point c such that
f'(c)=0

this is rolle theorem


please mark as brainliest

Answer 2

Hello!

$\boxed{\textbf{Rolle\:'\:s\:Theorem}}$

Let $\textbf{a}$ < $\textbf{b}$.

If $\textbf{f}$ is continuous on the closed interval $\textbf{[a, \:b]}$ and differentiable on the open interval $\textbf{(a,\: b)}$and $\textbf{f(a) = f(b)}$, then there is $\textbf{ (a,\: b)}$ with $\textbf{f\:' (c) = 0}$.

That means,

According to it, $\textbf{f}$ has a horizontal tangent somewhere between $\textbf{a}$ and $\textbf{b}$

Cheers!