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**1a2b3c2212****Member**- Registered: 2009-04-04
- Posts: 419

T>0, 0<x<1200.

How do I find the minimum value of T ?

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Hi 1a2b3c2212;

I hope you began by plotting T first. This will give you a rough estimate where the extrema are.

To find the minimum we diff. T with respect to x.

First term is easy:

For the next term:

We use the chain rule.

Say:

And

Then:

That's the first part of the chain rule formula. Now we need dT / du.

We have everything we need, start plugging in.

To find the maxima or minima you look for where the derivative is equal to 0. So set dT / dx = 0 and solve and you will have your minima. You should already know where it is approximately.

Post if you get stuck in solving.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**soroban****Member**- Registered: 2007-03-09
- Posts: 452

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**1a2b3c2212****Member**- Registered: 2009-04-04
- Posts: 419

Thanks soroban!

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