The number of admissible values of $C$ obtained when the Lagrange's mean value theorem is applied for the function $f(x)=x$ on $[2,5]$ is

If $f(x) = x^2 - 2x + 4$ and $\frac{f(5) - f(1)}{5 - 1} = f'(c)$,then the value of $c$ will be

For the function $f(x) = e^x$ on the interval $[a, b]$ where $a = 0$ and $b = 1$,the value of $c$ in the Lagrange's Mean Value Theorem is:

If $L.M.V.T.$ is true for $f(x) = x(x-1)(x-2)$ on the interval $x \in [0, 1/2]$,then find the value of $C$.

Let $S$ be the set of all functions $f:[0,1] \rightarrow \mathbb{R}$ which are continuous on $[0,1]$ and differentiable on $(0,1)$. Then for every $f \in S$,there exists a $c \in (0,1)$,depending on $f$,such that:

For the function $f(x) = x + \frac{1}{x}$,$x \in [1, 3]$,the value of $c$ for the Mean Value Theorem is: