If the function $$f(x) = 2{x^3} - 9a{x^2} + 12{a^2}x + 1$$ [a > 0] attains its maximum and minimum at p and q respectively such that p² = q, then a is equal to

Let f(x) > 0 for all x and f'(x) exists for all x. If f is the inverse function of h and $${h'(x) = {1 \over {1 + \log x}}}$$. Then, f'(x) will be

Let f(x) be a derivable function, f'(x) > f(x) and f(0) = 0. Then,

Let $$f(x) = {x^4} - 4{x^3} + 4{x^2} + c,\,c \in R$$. Then