1. Find the local maxima of the function: (1) f(x,y) = xy, subject to the constraint...

1. Find the local maxima of the function:

(1) f(x,y) = xy, subject to the constraint that x+y-1=0. Result should be 1/4.

2. Find the local minima of the functions:

(1) f(x,y) = x^2+y^2, subject to the constraint that xy-3=0. Result should be 6.

(2) f(x,y) = x^2+4xy+y^2, subject to the constraint that x-y-6=0. Result should be -18.

Solutions

Expert Solution

To calculate local maxima or local minima, first convert the function into single variable using the given constraint equation. Then find the minima or maxima of a function of single variable by differentiating the function with respect to that variable.

milcah answered 1 year ago

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