Question

Given the derivative of a function, how would I find the increasing and decreasing intervals of the function? I have not learned how to take the integral of the derivative yet, so was wondering if there's another way.

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Answer 1

Ah okay then xD

Answer 2

f increasing implies f' is positive.
f decreasing implies f' is negative.

Answer 3

so find the zeros of the derivative and figure out where the derivative is positive/negative

Answer 4

We're given the derivative though, and usually I would test out values between the intervals created by the zeros to see where the function's +/-. Except that doesn't work in this case because I would need the original function to plug in values to test.

Answer 5

You don't need the original function. If the derivative is positive, then the original function is increasing.

Answer 6

But I'm looking for the intervals where it increases/decreases..

Answer 7

That is, the intervals where the derivative is positive/negative. Follow zzr0ck3r's second answer.

Answer 8

So the zeros are 1, -2 and -3. Therefore the function increases when x >1, and decreases at -3 < x < -2?

Answer 9

Not sure how to 'figure out' the intervals from just the zeros.

Answer 10

The roots are correct. You are right about the interval x > 1. I think it's increasing on that second interval -3 < x < -2 because if you plug in something slightly smaller than -2 for x, the first two factors are negative so their product is positive. The third factor is also positive, so the derivative is positive.

Answer 11

The intervals are x < -3, -3 < x < -2, -2 < x < 1, x < 1.

Answer 12

So as you can see, the roots 'cut' the real number line into the intervals.

Answer 13

I have to go now so if you want do ask something do it quickly.