MATA33H3 Lecture Notes - Lecture 21: Lagrange Multiplier
17.7 – Lagrange Multipliers
Definition:
o is called the Lagrange Multiplier.
o A technique/method to find and optimize local extrema of a function of > 2 variables
where the function is subject to > 1 constraint equations
o Max and Min of f (x,y,z) are subjects to one constraint g(x,y,z) = K
1. Method of lagrange multipliers for one constraint:
a. To find max and min of f (x,y,z) subject to one constraint g(x,y,z) = K
(assume extreme values exist and g is not 0 on the surface g (x,y,z) = K)
b. Find all values of x, y, z /
c. Evaluate f @ all points ( x, y, z ) that result from the step above then:
i. Largest of these values = max of f
ii. Smallest of these values = min of f
APPLICATION EXAMPLE:
Compute the max and min of function f (x, y) = x^2 + y^2
fx = gx
fy = gy
fz = gz
3
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