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the graph is for f'(x). f(x) increases when f'(x) is positive and decreases when it's negative.

are my answers correct?

no. you gave intervals where the derivative increases/decreases

do you understand why your answer is wrong and how to get the correct intervals?

I understand why its wrong, but Im not sure how to get the right intervals

f will increase on intervals where the graph is positive and decrease where the graph is negative.

For example the graph is positive from 0 to 1, so f increases on the interval [0, 1).

oh okay i think i understand, um so for a it would be (3,5)?

and (0,1)

yes

and for b it would be (1,3) and (5,6)

yes, although I think you should use brackets [] for the 0 and 6 because of the closed circles.

okay so it would be 1,3 and 5?

yes

Thank you!!

you're welcome