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Math Help - Average Value of f

  1. #1
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    Average Value of f

    Suppose that f is a linera function. Using the graph of F explain why the average value of F on [a,b] is

    f((a+b)/2)

    This is probably so simple. :/
    I know all the formula for average value of f(x) using integration 1/(b-a) X integral of the function with the limits.

    Somehow I just can't figure out how to explain this.
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  2. #2
    MHF Contributor Calculus26's Avatar
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    See attachment
    Attached Thumbnails Attached Thumbnails Average Value of f-linear.jpg  
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  3. #3
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    The question stated, "Using the graph of F explain... "
    Does that solution still hold if they ask to use the graph to explain?
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  4. #4
    MHF Contributor Calculus26's Avatar
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    Using the graph the average value is the midpoint

    fave = [f(a) + f(b)]/2 = [Ma+ B + Mb +B] = M/2(a+b) + B = f((a+b)/2)
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