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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 for b it would be (1,3) and (5,6)
At what values of x does f have a local maximum or minimum? (Enter your answers as a comma-separated list.) Im not really sure how to solve for this part
yes, although I think you should use brackets  for the 0 and 6 because of the closed circles.
local maximums and minimums are where the derivative is 0, so pick out the x-intercepts of your graph
okay so it would be 1,3 and 5?