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Q. 20

Expert-verifiedFound in: Page 985

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, $f(x,y),$subject to the constraint that $(x,y)$is a point on the boundary of a triangle $\mathcal{T}$in the *xy*-plane.

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 $\mathcal{T}$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.

Given Function $f(x,y)$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.

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 $\mathcal{T}$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.

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