Analyzing functions max and min

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. f 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

Evaluating the statements:

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). We don't know...
2. If f '(x) > 0 on the interval (a, b), then f is decreasing on the interval (a, b). No, if f' is positive, the function is decreasing...
3. f f and g are increasing on the interval (a, b), then f + g is increasing on (a, b). Yes, if both functions are increasing, then the additive function is increasing...
4. None of these are true. See statement 3...