math question 3- very urgent !

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Find x* on [0, 2] such that f(x*) equals the average value of f(x) = 5x + 9 over [0, 2].

  • math question 3- very urgent ! -

    Tha average value of f is the integral of the function (over that [0,2] interval) divided by the interval width, 2.

    I assume you know how to integrate the function. The value of the integral is
    5/2*4 + 18 = 28 . The average value is therefre 28/2 = 14

    Now find what value of x that makes
    5x + 9 = 14. It is 1

    That should not be a surprise. For a linear function, the average is the value in the middle of the interval.

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