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Thread: [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 $\displaystyle f(x)$ on a generalized interval $\displaystyle [a,b]$ is given by

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

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

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

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

    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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    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 $\displaystyle c\neq6$, the average will be smaller since either more points will be below the maximum (for $\displaystyle c > 6$) or the maximum will be lower (for $\displaystyle c < 6$).

    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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