Question: Let a, b, c, D, E be real numbers with c 0. a) If DE > 0, find all extrema of ax + by

Let a, b, c, D, E be real numbers with c ≠ 0.
a) If DE > 0, find all extrema of ax + by + cz subject to the constraint z = Dx2 + Ey2. Prove that a maximum occurs when cD < 0 and a minimum when cD > 0.
b) What can you say when DE < 0?

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a The Lagrange equations are a 2Dx b 2Ey and c Thus ... View full answer

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