If `f(x)=|x|^3` , show that `f"(x)` exists for all real `x` and find it.

If f(x)=|x|^(3) show that show that exists for all real x and find it.

If f is a real function such that f(x)>0,f'(xx) is continuous for all real x and axf'(x)>=2sqrt(f(x))-2af(x),(ax!=2) show that sqrt(f(x))>=(sqrt(f(1)))/(x),x>=1

If f(x) satisfies the relation 2f(x)+(1-x)=x^(2) for all real x, then find f(x) .

If f(x)=x*x 1) and f'(x) exists finitely for all x in R, then

Let (f(x+y)-f(x))/(2)=(f(y)-a)/(2)+xy for all real x and y. If f(x) is differentiable and f'(0) exists for all real permissible value of a and is equal to sqrt(5a-1)-a^(2). Then f(x) is positive for all real xf(x) is negative for all real xf(x)=0 has real roots Nothing can be said about the sign of f(x)

A function f:R rarr R satisfies the relation f((x+y)/(3))=(1)/(3)|f(x)+f(y)+f(0)| for all x,y in R. If f'(0) exists,prove that f'(x) exists for all x,in R

If f(x)=(|x-a|)/(x-a) , then show that lim_(xrarra) f(x) does not exist.

Let f:R rarr R be a twice differentiable function such that f(x+pi)=f(x) and f'(x)+f(x)>=0 for all x in R. show that f(x)>=0 for all x in R .

Let h(x)=f(x)-a(f(x))^(2)+a(f(x))^(3) . If h(x) increases as f(x) increases for all real values of x if