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Math Help - [SOLVED] average value

  1. #1
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    [SOLVED] average value

    Let A represent the average value fo the function f(x) on the interval [0,6]. Is there a value of c for which the average value of f(x) on the interval [0,c] is greater than A? Why or why not?



    I really hv no idea how to do this problem. Looking at the graph, I thot that there is a value of c because at x=7 the area is greater than x=6? but that's totally just a guess
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  2. #2
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by chukie View Post
    Let A represent the average value fo the function f(x) on the interval [0,6]. Is there a value of c for which the average value of f(x) on the interval [0,c] is greater than A? Why or why not?



    I really hv no idea how to do this problem. Looking at the graph, I thot that there is a value of c because at x=7 the area is greater than x=6? but that's totally just a guess
    You tell us, average value of a function f(x) on a generalized interval [a,b] is given by

    \frac{1}{b-a}\int_a^{b}f(x)dx...Now think, graphically will there be a point \in[a,b] such that

    f(c)>\frac{1}{b-a}\int_a^{b}f(x)dx?
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  3. #3
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    Quote Originally Posted by Mathstud28 View Post
    You tell us, average value of a function f(x) on a generalized interval [a,b] is given by

    \frac{1}{b-a}\int_a^{b}f(x)dx...Now think, graphically will there be a point \in[a,b] such that

    f(c)>\frac{1}{b-a}\int_a^{b}f(x)dx?

    umm no there isnt a value of c? because at x=6 it's already at a maximum? im not sure if im thinking in the right direction
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    MHF Contributor Reckoner's Avatar
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    Quote Originally Posted by chukie View Post
    umm no there isnt a value of c? because at x=6 it's already at a maximum? im not sure if im thinking in the right direction
    Your reasoning is fine. For any c\neq6, the average will be smaller since either more points will be below the maximum (for c > 6) or the maximum will be lower (for c < 6).

    You could make this a bit more formal, but I think a simple explanation is probably all that the question is after.
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