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The integral of that curve, f' over any interval will tell you the increase or decrease of f. If it's area above the axis, that's an increase of f. If it's area below the axis, that's a decrease of f. The important places to check f are the endpoints and wherever f' is 0.
Also since is the graph of the derivative, look at the zeros and where this graph of the derivative changes from a + to a neg (Like Smoothmath said) Don't forget the initial value also.
haha... that looks like a sample AP exam question...
Yup. I'm teaching AP calc at the moment, and I just gave my students this problem as review before the AP test.
the test is this Wednesday?
When I added the negative and positive values I came up with: 20-6+4=18, then I added the initial 2, but that gives me 20 and it says the answer is 22
That's the integral over the WHOLE interval, which means it ends up there, at 20. Perhaps it gets further at an earlier time?
that's because the question is asking what is the maximum f will get in the interval. your answer is at the end of the interval.
Look at other intervals and ask yourself where the partical is at those times.
Wait is it 22 because the largest area is 20 and adding the initial 2 gives 22 as the answer?
Oh, sorry it didn't notify me. Yeah, it's 22. You need to check at each value that the derivative is 0.
So I just find the largest value where the derivative is 0 and add the initial value on, right?
Notice the points that I checked f at. The endpoints, and every point where f'=0.
So, just 20+2?