If $f:R \to R$ and $f(x)$ is a polynomial function of degree ten with $f(x)=0$ has all real and distinct roots. Then the equation ${\left( {f'\left( x \right)} \right)^2} - f\left( x \right)f''\left( x \right) = 0$ has
no real roots
$10$ real roots
$6$ real roots
$8$ real roots
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
For the function$x + {1 \over x},x \in [1,\,3]$, the value of $ c$ for the mean value theorem is
Verify Rolle's theorem for the function $y=x^{2}+2, a=-2$ and $b=2$
Rolle's theorem is true for the function $f(x) = {x^2} - 4 $ in the interval
Suppose that $f$ is differentiable for all $x$ and that $f '(x) \le 2$ for all x. If $f (1) = 2$ and $f (4) = 8$ then $f (2)$ has the value equal to