mean-value-of-a-function

Mean value of a function

What is the mean value of a function?

• The mean value of a function may be thought of as the ‘average’ value of a function over a given interval

• For a function f(x), the mean value of the function over the interval [a, b] is given by

  

  • Note that the mean value  is simply a real number – it is not a function

  • The mean value depends on the interval chosen – if the interval [a, b] changes, then the mean value may change as well

• Because  is a real number, the graph of is a horizontal line

  • This gives a geometrical interpretation of the mean value of a function over a given interval

  • If A is the area bounded by the curve y = f(x), the x-axis and the lines x = a and x = b, then the rectangle with its base on the interval [a, b] and with height also has area A

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