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Calculus/optimization problems

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Expert: - 10/9/2008


Question
I'm sure this is easy but I am terrible with calculus.

Find the minimum of Q = x2(squared) + y2(squared)
if x + y = 6


Answer
Take the function and substitute in 6-x for y.  This will give you a function of x only.

There is no need to square out 6-x in the equation, but just go ahead and take the derivative of the problem as is, that is, the derivative of x² + (6-x)².

The derivative of x² is 2x and the derivative of (6-x)² is (6-x)(-1).
We know that the entire derivative is then 2x -(6x-1).  

This can be set to 0 and a solution can be found.

Once x is know, y is 6-x.

Computer usage
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For future reference, ² is alt-253; √ is alt-251.
Some people just put x^2 for x squared.

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