`f(x)= x^(3)` sgn(x). Show that f(x) is differentiable at x=0.

Show that f(x) = |x| sin x is differentiable at x=0.

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.

If f(x) = x^(3) sgn (x), then

If f(x) = 0 for x lt 0 and f(x) is differentiable at x = 0, then for x gt 0, f(x) may be

A function f: R rarr R satisfies the equation f(x+ y)= f(x).f(y) "for all" x, y in R, f(x) ne 0 . Suppose that the function is differentiable at x=0 and f'(0)=2, then prove that f'(x)= 2f(x)

A function f : R rarr R satisfies the equation f(x + y) = f(x) . f(y) for all, f(x) ne 0 . Suppose that the function is differentiable at x = 0 and f'(0) = 2. Then,

If for all x,y the function f is defined by f(x)+f(y)+f(x).f(y)=1 andf(x)gt0. Then show f'(x)=0 when f'(x)=0 is differentiable.

Statement I f(x) = |x| sin x is differentiable at x = 0. Statement II If g(x) is not differentiable at x = a and h(x) is differentiable at x = a, then g(x).h(x) cannot be differentiable at x = a