Use Lagrange multipliers to find the maximum and minimum values of the function subject to the given constraints.
f(x,y) = 4x + 6y; x^2 + y^2 = 13
I'm not sure how to solve this.
Do you know how to use Lagrange Multipliers? Basically let us define and . We then need to solve the system of equations given by
A little work shows the above is equivalent to
And unless my calculations are off I calculate the solutions to be
So now and . From there we can conclude that the point is a minimum point and a maximum point.
Hello, paulrb!
I must assume you know the basic steps for Lagrange multipliers.
Use Lagrange multipliers to find the maximum and minimum values
of the function subject to the given constraints.
. .
We have: .
Take partial derivatives and equate to zero.
. . .[1]
. . .[2]
. . .[3]
Substitute [1] and [2] into [3]: .
. . . . . .
Substitute into [1]: .
Substitute into [2]: .
. .