Let f(x) (x², if x is rational, = 0, if x is irrational Show that is differentiable at x = 0, and find f'(0).

If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local extremum offon (a,c) ?

Is there a real function f(x) that is differentiable only at a point x?

Suppose f is differentiable on the set of real numbers R and a E R. Let F(x) f(x") and G(r) = [f(x)]a. Find expressions for F"(x) and G" (x).