Homework Help: geometric mean

Posted by Jen on Sunday, November 5, 2006 at 8:58pm.

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 - wertw, Tuesday, January 29, 2008 at 5:22pm
etyhw
- geometric mean - keisha, Friday, March 7, 2008 at 2:04pm
  need the geometric mean for 4 and 6
geometric mean - ppkh, Thursday, July 19, 2012 at 1:20am
f(b)-f(a)
________ = f'(c)
b-a

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

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