Let $f$ be any function defined on $R$ and let it satisfy the condition

$|f( x )-f( y )| \leq\left|( x – y )^{2}\right|, \forall( x , y ) \in R$ If $f(0)=1,$ then

Let $f(x) = \sqrt {x – 1} + \sqrt {x + 24 – 10\sqrt {x – 1} ;} $ $1 < x < 26$ be real valued function. Then $f\,'(x)$ for $1 < x < 26$ is

If $f$ is a differentiable function such that $f(2x + 1) = f(1 -2x)$ $\forall \,\,x \in R$ then minimum number of roots of the equation $f'(x) = 0$ in $x \in \left( { – 5,10} \right)$ ,given that $f(2) = f(5) = f(10)$ , is

Examine if Rolle's Theorem is applicable to any of the following functions. Can you say some thing about the converse of Roller's Theorem from these examples?

$f(x)=[x]$ for $x \in[5,9]$

In which of the following functions Rolle’s theorem is applicable ?