Consider the function $f (x) = 8x^2 - 7x + 5$ on the interval $[-6, 6]$. The value of $c$ that satisfies the conclusion of the mean value theorem, is

If the function $f(x) = a{x^3} + b{x^2} + 11x - 6$ satisfies the conditions of Rolle's theorem for the interval $[1, 3$] and $f'\left( {2 + \frac{1}{{\sqrt 3 }}} \right) = 0$, then the values of $a$ and $b$ are respectively

If $L.M.V.$ theorem is true for $f(x) = x(x-1)(x-2);\, x \in [0,\, 1/2]$ , then $C =$ ?

Let $f(x) = 8x^3 - 6x^2 - 2x + 1,$ then

Let $\mathrm{f}$ be any continuous function on $[0,2]$ and twice differentiable on $(0,2)$. If $\mathrm{f}(0)=0, \mathrm{f}(1)=1$ and $f(2)=2$, then

Which of the following function can satisfy Rolle's theorem ?