Define derivative of a function 'f' at x = c

Define the derivative of a function f(x) at an arbitrary point x in its domain of definition.

Let f (x) be a differentiable function and f '(1) =4,f'(2) =6 where f '(c ) means the derivative of function f(x) at x=c. Then lim _(hto0)(f(2 +2h +h^(2))-f(2))/(f (1+h-h^(2))-f(1)) is equal to-

The left hand derivative of the function y = f(x) at x = a is Lf' (a) =

The right hand derivative of the function y = f(x) at x = a is Rf' (a) =

Suppose the function f(x)-f(2x) has the derivative 5 at x=1 and derivative 7 at x=2 . The derivative of the function f(x)-f(4x) at x=1 has the value equal to (a) 19 (b) 9 (c) 17 (d) 14

If the derivative of a function is sqrt(x) , then the function is -

The derivative of the function f(x) =I x I^3 at x = 0 is

IS the derivative of the function f(x)=|x| at x=0.possible?

Statement 1: Let f: R -> R be a real-valued function AAx ,y in R such that |f(x)-f(y)|<=|x-y|^3 . Then f(x) is a constant function. Statement 2: If the derivative of the function w.r.t. x is zero, then function is constant.

The derivative of the function f(x)=3|x+2| at the point, x = -3 is -