Find the extreme values of the function f(x, y) = 4x2 + 6y2 on the circle x2 + y2 = 1.

Answer with Step-by-step explanation:

We are given that

Let g(x,y)=

We have to find the extreme values  of the given function

Using Lagrange multipliers

Possible value x=0 or

If x=0 then substitute the value in g(x,y)

Then, we get

If and substitute in the equation

Then , we  get possible value of y=0

When y=0 substitute in g(x,y) then we get

Hence, function has possible  extreme values at points (0,1),(0,-1), (1,0) and (-1,0).

Therefore, the maximum value of f  on the circle  is and minimum value of

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