Thursday

November 27, 2014

November 27, 2014

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

**Answer this Question**

**Related Questions**

Geometry-8th gr - The geometric mean x of two numbers is the positive value of x...

math - What is the difference between geometric mean and arithmetic mean? ...

arithmetic - 1. The first and last term of an A.P are, a and l respectively, ...

arithmetic - 1. The first and last term of an A.P are, a and l respectively, ...

math - if the arithmetic mean of 2 positive numbers (a and b) is 16 and their ...

Math *URGENT - Please give the answers and solutions for each. 1.If the second ...

geometric mean - Eighteen is the Geometric Mean of 12 and what number 18 = sqrt...

math - The arithmetic mean of two numbers is 9 and their geometric mean is 3&#...

geometry - in the proportion 2/8=8/32, which numbers is the geometric mean of ...

Algebra 2 - Find the geometric mean of each pair of numbers. 1/12, 1/18 I ...