f(x)=x/e^x

Question

Show that f is continuous and differentiable for all real numbers.

Answer 1

since e^x is never zero, it is clear that f(x) is continuous everywhere

so, what does it mean to be differentiable?

Answer 2

I believe it implies that the function can be differentiated

Answer 3

yes. That involves evaluating a limit. If that limit exists, then the function is differentiable.