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)| le sin ^(2) x, AA x in R, then

If y= f (x) is differentiable AA x in R, then

(i) if f ( (x + 2y)/3)]= (f(x) +2f(y))/3 , " x, y in R and f (0) exists and is finite ,show that f(x) is continuous on the entire number line. (ii) Let f : R to R satisfying f(x) -f (y) | le | x-y|^(3) , AA x, y in R , The prove that f(x) is a constant function.

Let f(x) be a function satisfying f(x) + f(x+2) = 10 AA x in R , then

If f:Rrarr R is a function defined as f(x^(3))=x^(5), AA x in R -{0} and f(x) is differentiable AA x in R, then the value of (1)/(4)f'(27) is equal to (here f' represents the derivative of f)

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: Rvec satisfying |f(x)|lt=x^2AAx in R be differentiable at x=0. The find f^(prime)(0)dot

Let f :R to R be a function, such that |f(x)|le x ^(4n), n in N AA n in R then f (x) is:

Let f : R rarr R be defined by f(x) = x^(2) - 3x + 4 for all x in R , then f (2) is equal to

Let f: R->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) .