Calculus
posted by Scooby10 on .
What is the state of the function f at x = 2?
F(x) = [x^3 for x < 2; 5x  2 for x > or = to 2]
?continuous or differentiable both or neither one or the other?

F(x) is continuous at x=2, since
2^3 = 5*22 = 8
But, F' is not continuous, since
3*2^2 = 12
but
5 = 5