Which one of the following statements is true?

A. 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).

B. If f ' (x) > 0 on the interval (a, b), then f is decreasing on the interval (a, b).

C. If f and g are increasing on the interval (a, b), then f + g is increasing on (a, b). D. None of these are true.

Question

Bentley

Mathematics

9 October, 05:31

Which one of the following statements is true?

A. 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).

B. If f ' (x) > 0 on the interval (a, b), then f is decreasing on the interval (a, b).

C. If f and g are increasing on the interval (a, b), then f + g is increasing on (a, b). D. None of these are true.

+2

Answers (1)

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Kolten Caldwell · Answer 1

The answer is C) If f and g are increasing on the interval (a, b), then f + g is increasing on (a, b).

If f' (x) >0 on the interval, and f' (g) >0, then f' + g' > 0 on the interval as well. If both functions are increasing on the interval, then their sum is increasing as well.

A is wrong because the absolute max/min could be outside the interval (a, b).

B is wrong because is f' (x) >0, then f is increasing on the interval.