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CalculusInt Group Title

How would I solve this problem: (problem attached)

  • 2 years ago
  • 2 years ago

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  1. CalculusInt Group Title
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    • 2 years ago
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  2. SmoothMath Group Title
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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.

    • 2 years ago
  3. TransendentialPI Group Title
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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.

    • 2 years ago
  4. dpaInc Group Title
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    haha... that looks like a sample AP exam question...

    • 2 years ago
  5. SmoothMath Group Title
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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.

    • 2 years ago
  6. dpaInc Group Title
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    the test is this Wednesday?

    • 2 years ago
  7. SmoothMath Group Title
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    Haha yes.

    • 2 years ago
  8. CalculusInt Group Title
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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

    • 2 years ago
  9. SmoothMath Group Title
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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?

    • 2 years ago
  10. dpaInc Group Title
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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.

    • 2 years ago
  11. SmoothMath Group Title
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    Look at other intervals and ask yourself where the partical is at those times.

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

    • 2 years ago
  13. CalculusInt Group Title
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    @SmoothMath @dpaInc

    • 2 years ago
  14. SmoothMath Group Title
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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.

    • 2 years ago
  15. CalculusInt Group Title
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    So I just find the largest value where the derivative is 0 and add the initial value on, right?

    • 2 years ago
  16. SmoothMath Group Title
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    |dw:1336438693557:dw|

    • 2 years ago
  17. SmoothMath Group Title
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    Notice the points that I checked f at. The endpoints, and every point where f'=0.

    • 2 years ago
  18. CalculusInt Group Title
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    So, just 20+2?

    • 2 years ago
  19. SmoothMath Group Title
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    Right.

    • 2 years ago
  20. CalculusInt Group Title
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    Thank you!

    • 2 years ago
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