Sumários

Exercises on Lagrange multipliers

12 Maio 2021, 09:30 • Rita Sousa

In this class we solved in class several exercises on Lagrange multipliers pertaining to the plan of Week 12 of the course. In particular, we solved the following exercises: (can be found in OneNote class link)

- 1.1 Find maxima and minima of f(x,y)=x^2-y^2, subject to g(x,y)=x^2+y^2=1

- 1.2. Find maxima and minima of f(x,y)=exp(xy) subject to g(x,y)=x^3+y^3=16

- Exercise 3: Show that the maximal area of a triangle with a given perimeter is obtained by the equilateral triangle.

- Exercise 2: Show that f(x,y)=x^2+y^2 subject to g(x,y)=xy=1 does not have a maximum, even though its optimization can be treated with Lagrange Multipliers