Rolle's theorem is true for the function $f(x) = {x^2} - 4 $ in the interval
$[-2, 0]$
$[-2, 2]$
$\left[ {0,\,{1 \over 2}} \right]$
$[0,\,\,2]$
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 $x \in[5,9]$
Which of the following function can satisfy Rolle's theorem ?
The number of polynomials $p: R \rightarrow R$ satisfying $p(0)=0, p(x)>x^2$ for all $x \neq 0$ and $p^{\prime \prime}(0)=\frac{1}{2}$ is
If $L.M.V.$ theorem is true for $f(x) = x(x-1)(x-2);\, x \in [0,\, 1/2]$ , then $C =$ ?
Let $f(x) = (x-4)(x-5)(x-6)(x-7)$ then -