# Mean Value Theorem

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• Aug 13th 2009, 07:21 PM
goldenroll
Mean Value Theorem
I'm having trouble with this question on mean value theorem

1. x+(96/x) on interval [6,16]

the problem with this equation is i get 0/(10) and when i check the answer is 4sq.rt(6) I'm using the f(b)-f(a)/b-a so what am i'm missing?
• Aug 13th 2009, 08:31 PM
VonNemo19
Quote:

Originally Posted by goldenroll
I'm having trouble with this question on mean value theorem

1. x+(96/x) on interval [6,16]

the problem with this equation is i get 0/(10) and when i check the answer is 4sq.rt(6) I'm using the f(b)-f(a)/b-a so what am i'm missing?

$1-\frac{96}{x^2}=\frac{\left(16+\frac{96}{16}\right)-\left(6+\frac{96}{6}\right)}{16-6}$

Solve for x.

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• Aug 13th 2009, 08:37 PM
goldenroll
that comes out to (22-22)/10? because the answer in the book says it come out to 4sq.rt6,
• Aug 13th 2009, 08:41 PM
VonNemo19
Quote:

Originally Posted by goldenroll
that comes out to (22-22)/10? because the answer in the book says it come out to 4sq.rt6,

Exactly. But you have only done the right side of the equation...

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Hint hint...
• Aug 13th 2009, 08:45 PM
goldenroll
hahaha, I guess we just found out were I got lost at. when you say I have only done the right side of the equation what do you mean.
• Aug 13th 2009, 08:54 PM
VonNemo19
Quote:

Originally Posted by goldenroll
hahaha, I guess we just found out were I got lost at. when you say I have only done the right side of the equation what do you mean.

Equations have right sides, and then they have left sides. Soooooo, generally when we "solve" equations, we isolate the variable. In this case, the variable would be x. So, your task is to move everything to one side of the equation except x.

The MVT says that there will be at least one place in an interval [a,b] where the slope of the tangent line to the graph will have the same slope as the secant line through [a,f(a)] and [b,f(b)]. You have found the slope of the secant line. So, you're not done.

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• Aug 13th 2009, 09:04 PM
goldenroll
oh, lamo, well I finally got the right answer when I finished the other side lol. Oh and just realized where the thanks button was lol.
• Aug 13th 2009, 09:09 PM
VonNemo19
Quote:

Originally Posted by goldenroll
oh, lamo, well I finally got the right answer when I finished the other side lol. Oh and just realized where the thanks button was lol.

Good. I hate asking people for thank yous, and if I didn't help you, don't thank me. But I think that you'll find that once you start clicking that thank you button, people will start busting down your door trying to help you.

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