Question

How do you find the Rolles value theorem applies?

Answer 1

Rolle’s Theorem :

A special case of Lagrange’s mean value theorem is Rolle’s Theorem which states that:

If a function$f$ is defined in the closed interval$[a,b]$ in such a way that it satisfies the following conditions.

i) The function$f$ is continuous on the closed interval $[a,b]$.

ii)The function$f$ is differentiable on the open interval $(a,b)$.

iii) Now if $f\left(a\right)=f\left(b\right)$ ,

then there exists at least one value of $x$, let us assume this value to be $c$, which lies between $a$ and $b$ i.e. $(a<c<b)$ in such a way that $f\text{'}\left(c\right)=0$.