Let `f: R->R` satisfying `|f(x)|lt=x^2,AAx in R` be differentiable at `x=0.` Then find `f^(prime)(0)dot`

Let f : R rarr R satisfying |f(x)|le x^(2), AA x in R , then show that f(x) is differentiable at x = 0.

Let f (x)=xabsx,AAx in R . Then,

Let f:R rarr R satisfying f((x+y)/(k))=(f(x)+f(y))/(k)(k!=0,2). Let f(x) be differentiable on R and f'(0)=a then determine f(x)

Let f(x y)=f(x)f(y)\ AA\ x ,\ y in R and f is differentiable at x=1 such that f^(prime)(1)=1 also f(1)!=0 , f(2)=3 , then find f^(prime)(2) .

Let f : R rarr R satisfying l f (x) l <= x^2 for x in R, then (A) f' is continuous but non-differentiable at x = 0 (B) f' is discontinuous at x = 0 (C) f' is differentiable at x = 0 (D) None of these

A function f(x) is differentiable at x=c(c in R). Let g(x)=|f(x)|,f(c)=0 then

Let f : R to R be a function such that f(x+y) = f(x)+f(y),Aax, y in R. If f (x) is differentiable at x = 0, then

A function f:R rarr R satisfy the equation f(x).f(y)=f(x+y) for all x,y in R and f(x)!=0 for any x in R. Let the function be differentiable at x=0 and f'(0)=2, Then : Then :

Let f be a differentiable function satisfying f(x/y)=f(x)-f(y) for all x ,\ y > 0. If f^(prime)(1)=1 then find f(x)dot

Let f:R to R be a function such that f(x+y)=f(x)+f(y)"for all", x,y in R If f(x) is differentiable at x=0. then, which one of the following is incorrect?