Some questions on the connections between continuity and differentiability. Important for your future, regardless of where life takes you.
1) What criteria must be met for a function to be considered continuous at a point where x=a?
2) What does it mean for a function to be considered differentiable at a point where x=a?
3) If a function is continuous everywhere, will it always be differentiable everywhere?
4) If a function is differentiable everywhere, will it always be continuous everywhere?
5) If a function is differentiable everywhere, will its derivative always be continuous everywhere?