- #1
magorium
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Homework Statement
Show that , the maximum value of function f(x,y) = x^2 + y^2 is 70 and minimum value is 20
in constraint below.
Homework Equations
Constraint : 3x^2 + 4xy + 6y^2 = 140
The Attempt at a Solution
Book's solution simply states the Lagrange rule as :
h(x , y ; L) = x^2 + y^2 - L(3x^2 + 4xy + 6y^2 - 140)
Takes partial derivatives for x , y and L.
h's partial derivative for x = 2x + L(6x + 4y) = 0
h's partial derivative for y = 2y + L(4x + 12y) = 0
h's partial derivative for L = 3x^2 + 4xy + 6y^2 -140 = 0
Then he takes the coefficients determinant of first two equations ( h derv for x , h derv for y)
|1+3L 2L |
|2L 1+6L |
And makes this determinant equal to zero , finds values for L.
The part i don't understand is , why he uses Cramer rule to the first two equations and equals it to zero ?