If c is a point at which Rolle's theorem holds for the function,
f(x) = $${\log _e}\left( {{{{x^2} + \alpha } \over {7x}}} \right)$$ in the interval [3, 4], where a $$ \in $$ R, then ƒ''(c) is equal to

Let ƒ(x) = xcos^–1(–sin|x|), $$x \in \left[ { - {\pi \over 2},{\pi \over 2}} \right]$$, then which of the following is true?

The value of c in the Lagrange's mean value theorem for the function
ƒ(x) = x³ - 4x² + 8x + 11, when x $$ \in $$ [0, 1] is:

Let ƒ(x) be a polynomial of degree 5 such that x = ±1 are its critical points.

If $$\mathop {\lim }\limits_{x \to 0} \left( {2 + {{f\left( x \right)} \over {{x^3}}}} \right) = 4$$, then which one of the following is not true?