Math Problem Statement

Use Lagrange multipliers to find the maximum and minimum values of f(x,y)=2x+y subject to x2+y2=5 Question 19Answer

a. 10, -10

b. 10.5, -10.5

c. 5, -5

d. 5.5, -5.5

Solution

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Math Problem Analysis

Mathematical Concepts

Optimization
Lagrange Multipliers
Multivariable Calculus

Formulas

f(x, y) = 2x + y
g(x, y) = x^2 + y^2 - 5 = 0
Lagrange multiplier method

Theorems

Lagrange Multiplier Theorem

Suitable Grade Level

Grades 11-12 (Advanced Calculus/Multivariable Calculus)