We let f(x) = e-1/x, x > 0 and f(0) = 0. Is f continuous at 0 or not? Prove your assertions

Determine whether each of the following statements is true or false and explain why. The derivative of a function exists whenever the function is continuous.

If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local extremum offon (a,c) ?