Explain how you could use the method of Lagrange multipliers to find the extrema of a function of two variables, $f (x, y),$ subject to the constraint that $(x, y)$ is a point on the boundary of a triangle $T$ in the xy-plane.

Question

Accepted Answer

Steps to find the extrema of the function $f (x, y)$ subject to the constraint that $(x, y)$ is on the boundary of the triangle $T$ are following.

Determine the gradient of the function.
equate the gradient of the function to zero and determine the critical points.
Checked whether the critical points fall in the triangle or not.
Take the critical points that fall on the boundary of the triangle and find function values.
The greatest and lowest function value are the extrema of the function.

Short Answer