Find the extreme values of f on the region described:
f(x,y)=x^2+y^2+4x-4y; x^2+y^2

Question

Find the extreme values of f on the region described:
f(x,y)=x^2+y^2+4x-4y; x^2+y^2<=9

anonymous · Answer

$$f(x,y)=x ^{2}+y ^{2}+4x-4y; \ x ^{2}+y ^{2}\le9 $$ We just learned lagrange multipliers and I know how to solve a typical problem with them, just not sure about how to solve inequalities with them.

anonymous · Answer

@UnkleRhaukus @amistre64 @eseidl @myko @Zarkon @phi

phi · Answer

This site explains how http://mat.gsia.cmu.edu/classes/QUANT/NOTES/chap4/node6.html It looks like you look for the extreme values without reference to the constraint, then check to see if the points also satisfy the constraint. Then analyze using lagrange multiplier. The idea is that either the constraint does not matter (i.e. the extreme value is within the allowed region) or the constraint does matter, in which case you are "on the constraint"