Given a differentiable function `f(x)` defined for all real `x`, and is such that `f(x+h)-f(x) <= 6 h ^2` for all real h and x. Show that `f(x)` is constant.

Given that f is a real valued differentiable function such that f(x) f'(x) lt 0 for all real x, it follows that

A differentiable function f defined for all x > 0 and satisfies f(x^2)=x^3 for all x > 0. What is the value f'(16) ?

Let f be a differentiable function defined on R such that f(0) = -3 . If f'(x) le 5 for all x then

Let f be a twice differentiable function defined on R such that f(0) = 1, f'(0) = 2 and f '(x) ne 0 for all x in R . If |[f(x)" "f'(x)], [f'(x)" "f''(x)]|= 0 , for all x in R , then the value of f(1) lies in the interval:

Let f(x) be continuous and differentiable function for all reals and f(x + y) = f(x) - 3xy + f(y). If lim_(h to 0)(f(h))/(h) = 7 , then the value of f'(x) is

If the function f defined on R-{0} is a differentiable function and f(x^3)=x^5 for all x, then f'(27)=

Let f(x) be continuous and differentiable function for all reals and f(x + y) = f(x) - 3xy + ff(y). If lim_(h to 0)(f(h))/(h) = 7 , then the value of f'(x) is

Let f(x) be continuous and differentiable function for all reals and f(x + y) = f(x) - 3xy + ff(y). If lim_(h to 0)(f(h))/(h) = 7 , then the value of f'(x) is

Let f(x) be continuous and differentiable function for all reals and f(x + y) = f(x) - 3xy + ff(y). If lim_(h to 0)(f(h))/(h) = 7 , then the value of f'(x) is

A differentiable function f defined for all x>0 satisfies f(x^(2)) = x^(3) for all x>0. what is f'(b)?