Finding the absolute max and min on a constraint

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seven

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Find the absolute max and min of the function
x^2 + y^2 -6y + 9 that is subject to the constraint x^2 +y^2 =16
For each give the location as well as the max or min.
I really need help on how to go about solving this as I have an assignment filled with similar problems as this one.
 
Hello, and welcome to FMH! :)

Are you studying Lagrange Multipliers?
 
If \(\displaystyle x^2 + y^2 = 16\) is a constraint, does that mean that \(\displaystyle x^2 + y^2 = 16\)?
That is, shouldn't \(\displaystyle f(x,y) = 25-6y?\)
Is there a constraint on what y can be?
You have a line segment and just want the max and min for this line segment. It doesn't seem to hard to find. Please show us your work.
 
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