The temperature in the steam room of the Star Ship Enterprise is given by the following function:

Captain Kirk likes the hottest temperature while Mr Spock prefers the coolest area of the steam room.

Where should each of them sit? Why?

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- Jan 18th 2011, 04:10 AMTweetycalculus word problem help
The temperature in the steam room of the Star Ship Enterprise is given by the following function:

Captain Kirk likes the hottest temperature while Mr Spock prefers the coolest area of the steam room.

Where should each of them sit? Why? - Jan 18th 2011, 04:12 AMProve It
How would you normally go about minimising/maximising a two-variable function?

- Jan 18th 2011, 04:25 AMTweety
dont really remember, do I use partial derivatives?

- Jan 18th 2011, 04:42 AMProve It
Yes, you first need to find where , and then evaluate the Hessian at those points .

- Jan 18th 2011, 05:36 AMJester
Also, don't forget to check the boundary. The absolute min/max may lie there.

- Jan 18th 2011, 07:51 AMTweety
- Jan 18th 2011, 08:03 AMProve It
First, you need to find all the first and second partial derivatives.

Set the first partial derivatives equal to and solve for . Then substitute this value into the second partial derivatives (in the Hessian Matrix). If your Hessian is postive definite, you have a minimum. If it's negative definite, you have a maximum.

And like Danny said, you also need to check the boundaries.