Answer to Question #16607 in Real Analysis for katie

Question

Suppose f is a function such that
f(x) = { x^2, x element Q
0 x element R - Q

Is f continuous at c=0? is f differentiable at c = 0?

Answer 1

f(x) is discontinuous at all points of R, so it isn't continuous at c=0 and isn't differentiable at c = 0.