Direction : Consider the following for the items that follow :

Let f : (-1, 1) → R be a differentiable function with f(0) = -1 and f’(0) = 1 Let h(x) = f(2f(x) +2) and g(x) = (h(x))². 

Direction : Consider the following for the items that follow :

Let f : (-1, 1) → R be a differentiable function with f(0) = -1 and f’(0) = 1 Let h(x) = f(2f(x) +2) and g(x) = (h(x))². 

Consider the following for the next two (02) items that follow:

Let $f(x) = \frac{x}{\ln x}; (x > 1)$

Consider the following statements :
1. $f''(e) = \frac{1}{e}$
2. $f(x)$ attains local minimum value at $x = e$
3. A local minimum value of $f(x)$ is $e$
Which of the statements given above are correct ?

Consider the following for the next two (02) items that follow:

Let $f(x)$ and $g(x)$ be two functions such that $g(x) = x - \frac{1}{x}$ and $f \circ g(x) = x^3 - \frac{1}{x^3}$.

What is $f''(x)$ equal to?