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Question: Consider the function f(x,y,z) = x2 – y2 + z2 subject to the constraint x + 4z = 5 (a) f need n...

Consider the function f(x,y,z) = x² – y² + z² subject to the constraint x + 4z = 5

(a) f need not have an absolute maximum nor absolute minimum because x + 4z = 5 is a plane, which is not compact. Show that, in fact, f does not have an absolute minimum.

(b) f does have an absolute maximum. Use Lagrange multipliers to find where f has its absolute maximum.