Answer to Question #176063 in Calculus for Sourav Mondal

Question

Find the minimum value of the function 

f(x, y) = x²+ 2y²on the circle x² + y²= 1. 

Answer 1

Answer:1

GIVEN:

Function $f(x, y) = x²+ 2y²$ ...........................1

constraints $g(x, y) \implies x²+ y²=1$ ..................2

now,

Using Lagrange theorem for multipliers

we get x=1,-1

and y=0

so after putting points (1,0) and (-1,0)

we get minimum value of function as 1.