Question

Which one of the following statements is true?

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).

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

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

None of these are true.

Answer 1

I have no clue about any of these statements, if someone is willing to explain them, that would be ideal.

Answer 2

If I had to guess, I'd say the first statement seems true.

Answer 3

@Directrix

Answer 4

I think the second statement is false.

Answer 5

Not sure about the third.

Answer 6

If I had to guess, I'd go with the first one, but if anyone can give input that could steer me the right way, that would be appreciated.

Answer 7

If f(x) is increasing, and g(x) is increasing, then f(x) + g(x) is increasing.

TRUE: Since f; g are increasing, f'; g' are both positive so f' + g' is positive as well.

http://people.whitman.edu/~hundledr/courses/M125F11/M125/exam3revSOL.pdf

Answer 8

@Tahamohammed

Answer 9

That makes sense, but why would the first statement be false?

Answer 10

I don't see that this has to be true: If f is continuous on (a, b), then f attains an absolute maximum value.

Could it obtain an absolute minimum value?

And, the interval (a, b) is open and not closed as [a,b]. Doesn't that make a difference?