geometric mean

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The geometric mean of two postitive numbers a and b is sqrt(ab).
Show that for f(x) = 1/x on any interval [a,b] of positive numbers, the value of c in the conclusion of the mean value theorem is c = sqrt(ab)

I have no idea how to do this!

If the mean of a and b is sqrt(ab), then (a + b) / 2 = sqrt(ab).

Is c supposed to be the area under the graph in interval [a,b] ? If so, calculate the antiderivative of f(x) and you'll have the formula for c.

It is the geometric mean. Isn't (a+b)/2 the arithmetic mean?

  • geometric mean -

    etyhw

  • geometric mean -

    need the geometric mean for 4 and 6

  • geometric mean -

    f(b)-f(a)
    ________ = f'(c)
    b-a

    1/b - 1/a
    __________ = -1/(c)^2
    b-a

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