Use Lagrange multipliers to find the maximum and minimum values of f(x,y)=x+4y subject to the constraint x2+y2=9, if such values
exist. Round your answers to three decimal places. If there is no global maximum or global minimum, enter NA in the appropriate answer area. Maximum =
1 answer:
The Lagrangian is

with critical points where the partial derivatives vanish.



Substitute
into the last equation and solve for
:

Then we get two critical points,

We get an absolute maximum of
at the second point, and an absolute minimum of
at the first point.
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