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Expert-verified Found in: Page 985 ### Calculus

Book edition 1st
Author(s) Peter Kohn, Laura Taalman
Pages 1155 pages
ISBN 9781429241861 # Explain how you could use the method of Lagrange multipliers to find the extrema of a function of two variables, $f\left(x,y\right),$subject to the constraint that $\left(x,y\right)$is a point on the boundary of a triangle $\mathcal{T}$in the xy-plane.

Steps to find the extrema of the function $f\left(x,y\right)$subject to the constraint that $\left(x,y\right)$is on the boundary of the triangle $\mathcal{T}$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.
See the step by step solution

## Step 1. Given information.

Given Function $f\left(x,y\right)$subject to the constraint that $\left(x,y\right)$is a point on the

the boundary of a triangle $\mathcal{T}$in the xy-plane.

## Step 2. steps to find the extrema of a function.

Steps to find the extrema of the function $f\left(x,y\right)$subject to the constraint that $\left(x,y\right)$is on the boundary of the triangle $\mathcal{T}$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. ### Want to see more solutions like these? 