Let f(x) = x|x|, for all `x inR`. Discuss the derivability of f(x) at x = 0.

Discuss the differentiability of f(x)=|(log)_(e)x|f or x>0

If f(x) = {{:(x - 3",",x lt 0),(x^(2)-3x + 2",",x ge 0):}"and let" g(x) = f(|x|) + |f(x)| . Discuss the differentiability of g(x).

The derivative of f(x)=|x|^(3) at x=0, is

Let f(x)=x+(1)/(x),xne0. Discuss the maximum and minimum value of f(x).

Let f(x) be a differentiable function for all x in R The derivative of f(x) is an even function If the period of f(2x) is 1 then the value of f(2)+f(4)-f(6)-f(8) is.

If f(x)=(x)/(1+|x|)" for "x inR , then f'(0) =

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: