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I'm given a drawing of the graph $f '(x)= -x^2(x-5)$.
Given $f '(x)$ how do I find the $y$-intercept of $f(x)$?

I know the $x$-intercepts of $f '(x)$ give me my maximum and minimums for $f (x)$.

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    There are lots of possible f(x) that have that same f'(x) (You can get all the possibilities by shifting one f(x) up or down). Without knowing which f(x) you're dealing with (which you can find out if you're given any point on the graph of f(x)) you can't find the y-intercept. – 2017-02-10

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