Finding Relative Extrema of a Quadratic Function of Two Variables
Partial derivatives
warmup
Find all relative maxima and minima of \( f(x, y) = x^2 + 2xy + 2y^2 \).
multivariable-calculuspartial-derivativescritical-pointsrelative-extremaabsolute-minimumcompleting-the-squareoptimizationquadratic-formfind-minimumfind-maximum
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What you need first
- Partial differentiation
- Solving systems of linear equations
- Completing the square
What this problem tests
Tests the ability to compute partial derivatives, find critical points, and use algebraic manipulation (completing the square) to classify extrema.
This problem is typical of an introductory multivariable calculus course, introducing optimization of functions of two variables.
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