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?

## Answer This Question

## Related Questions

- Geometry-8th gr - The geometric mean x of two numbers is the positive value of x...
- algebra - 1. The geometric mean between the first two terms in a geometric ...
- math - What is the difference between geometric mean and arithmetic mean? ...
- Mathematics optimization - The arithmetic mean of two numbers a and b is the ...
- math - verify that the function satisfies the hypothesis of the mean value ...
- calculus - verify that the function satisfies the hypothesis of the mean value ...
- h.p. - the arithmetic mean of two numbers exceeds the geometric mean by 3/2 and ...
- Caluclus - [Mean Value Theorem] f(x)=-3x^3 - 4x^2 - 2x -3 on the closed interval...
- math - if the arithmetic mean of 2 positive numbers (a and b) is 16 and their ...
- math - verify that the function satisfies the hypotheses of the mean values ...

More Related Questions