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CalculusInt

How would I solve this problem: (problem attached)

  • one year ago
  • one year ago

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  1. CalculusInt
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    • one year ago
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  2. SmoothMath
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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.

    • one year ago
  3. TransendentialPI
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    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.

    • one year ago
  4. dpaInc
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    haha... that looks like a sample AP exam question...

    • one year ago
  5. SmoothMath
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    Yup. I'm teaching AP calc at the moment, and I just gave my students this problem as review before the AP test.

    • one year ago
  6. dpaInc
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    the test is this Wednesday?

    • one year ago
  7. SmoothMath
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    Haha yes.

    • one year ago
  8. CalculusInt
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    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

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

    • one year ago
  10. dpaInc
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    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.

    • one year ago
  11. SmoothMath
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    Look at other intervals and ask yourself where the partical is at those times.

    • one year ago
  12. CalculusInt
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    Wait is it 22 because the largest area is 20 and adding the initial 2 gives 22 as the answer?

    • one year ago
  13. CalculusInt
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    @SmoothMath @dpaInc

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

    • one year ago
  15. CalculusInt
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    So I just find the largest value where the derivative is 0 and add the initial value on, right?

    • one year ago
  16. SmoothMath
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    |dw:1336438693557:dw|

    • one year ago
  17. SmoothMath
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    Notice the points that I checked f at. The endpoints, and every point where f'=0.

    • one year ago
  18. CalculusInt
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    So, just 20+2?

    • one year ago
  19. SmoothMath
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    Right.

    • one year ago
  20. CalculusInt
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    Thank you!

    • one year ago
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