Wednesday

April 1, 2015

April 1, 2015

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

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 5:22pmetyhw

- geometric mean -
**keisha**, Friday, March 7, 2008 at 2:04pmneed the geometric mean for 4 and 6

- geometric mean -
- geometric mean -
**ppkh**, Thursday, July 19, 2012 at 1:20amf(b)-f(a)

________ = f'(c)

b-a

1/b - 1/a

__________ = -1/(c)^2

b-a

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