Need help of max and min calculus, thank you

Question

Which one of the following statements is true?

Options:

1. If f is continuous on (a, b), then f attains an absolute maximum value and f attains an absolute minimum inside the interval (a, b).
2. If f '(x) > 0 on the interval (a, b), then f is decreasing on the interval (a, b).
3. If f and g are increasing on the interval (a, b), then f + g is increasing on (a, b).
4. None of these are true.

Answer 1

1) An absurd statement....if a function is continuous, it can be any shape....I wonder if the intent was:

"If f is continuous on (a, b), AND f attains an absolute maximum value, THEN f attains an absolute minimum inside the interval (a, b)."---this still has a problem: one of the f's should be f'.

2) If the first derivative is positive, then the function is increasing

3) TRUE