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## CalculusInt 3 years ago How would I solve this problem: (problem attached)

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1. CalculusInt

2. SmoothMath

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.

3. TransendentialPI

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.

4. dpaInc

haha... that looks like a sample AP exam question...

5. SmoothMath

Yup. I'm teaching AP calc at the moment, and I just gave my students this problem as review before the AP test.

6. dpaInc

the test is this Wednesday?

7. SmoothMath

Haha yes.

8. CalculusInt

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

9. SmoothMath

That's the integral over the WHOLE interval, which means it ends up there, at 20. Perhaps it gets further at an earlier time?

10. dpaInc

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.

11. SmoothMath

Look at other intervals and ask yourself where the partical is at those times.

12. CalculusInt

Wait is it 22 because the largest area is 20 and adding the initial 2 gives 22 as the answer?

13. CalculusInt

@SmoothMath @dpaInc

14. SmoothMath

Oh, sorry it didn't notify me. Yeah, it's 22. You need to check at each value that the derivative is 0.

15. CalculusInt

So I just find the largest value where the derivative is 0 and add the initial value on, right?

16. SmoothMath

|dw:1336438693557:dw|

17. SmoothMath

Notice the points that I checked f at. The endpoints, and every point where f'=0.

18. CalculusInt

So, just 20+2?

19. SmoothMath

Right.

20. CalculusInt

Thank you!

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