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) ?

Show that the function f(x)=√x+1 is differentiable in z = 2 but not differentiable in x = -1.

Let f(x) = 2x³-7x² + 4x. a. On what interval(s) is f'(x) > 0? b. On what interval(s) is f(x) decreasing? c. On what interval(s) is f"(x) <0?