Math Problem Statement
Find the exact extreme values of the function z = f(x, y) = 3x^2 - 2xy + 4y^2 - 6x - 20y + 7 subject to the following constraints: 0 <= x <= 5 0 <= y <= 6 find the four boundary points and order your answers from smallest to largest x, then from smallest to largest y.
Solution
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Math Problem Analysis
Mathematical Concepts
Multivariable Calculus
Optimization
Boundary Evaluation
Formulas
f(x, y) = 3x^2 - 2xy + 4y^2 - 6x - 20y + 7
Theorems
Extreme Value Theorem
Boundary and Interior Extrema Theorems
Suitable Grade Level
Undergraduate Level (Calculus III or Multivariable Calculus)
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