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Math Help - concavity

  1. #1
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    concavity

    If n is a positive integer, how many times does the function f(x) = x^2 + 5cos(x) change concavity in the interval 0 is less than or equal to x which is less than or equal to 2*pi*n?
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by DINOCALC09 View Post
    If n is a positive integer, how many times does the function f(x) = x^2 + 5cos(x) change concavity in the interval 0 is less than or equal to x which is less than or equal to 2*pi*n?
    This is asking: How many times does f''(x) change sign in the interval [0, 2*n*pi].

    RonL
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  3. #3
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    ok the second derivative is 2-5cox(x)

    i graph it.

    and see that in between every 2pi it changes sign twice, so that means that the answer is it changes n-times as the answer?
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  4. #4
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    i think that the answer is 2

    anyone have any oppinoins?
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  5. #5
    Grand Panjandrum
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    Quote Originally Posted by DINOCALC09 View Post
    ok the second derivative is 2-5cox(x)

    i graph it.

    and see that in between every 2pi it changes sign twice, so that means that the answer is it changes n-times as the answer?
    It changes concavity twice in the interval [0,2 \pi], and as the second derivative is periodic with period 2 \pi in any of the intervals [2 n \pi, 2 (n+1) \pi], and most closed intervals of length 2 \pi (the exeptions are intervals with a zero of 2-5 \cos(x) at an end point.


    RonL
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