Question

Which one of the following statements is true? (4 points)

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.

I have no idea o-o

Answer 1

I gotta say, I also have no idea

Answer 2

Can you specify the choices\statements?

Answer 3

well, i honestly dont understand :\

Answer 4

"Which one of the following statements is true?"
where are the statements that we would check?

Answer 5

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.

Answer 6

so That makes sense now!

Answer 7

I think and believe about C, because for A it is not a condition to have maximum or minimum within the interval [a,b]

Answer 8

But I can't say that B is false

Answer 9

That is about B.
https://www.desmos.com/calculator/quf7githfj
f(x) increases, then f'(x) increases and vice versa!

Answer 10

you were right!
i got an A+, thank you so much ^-^

Answer 11

ohhhhh I see

Answer 12

Thanks for this question Volpina, and the answer 3mar

Answer 13

I am really happy to hear that.

Answer 14

Don't mention it sister @HannanSM!
I am here for your help.

Answer 15

Are you persuaded and satisfied, @volpina?

Answer 16

I took this subject last semester and it's nice to go back on it.

Answer 17

yes, thank you both so much :)

Answer 18

It's nothing.
I thank you that you gave me that chance to help you!