# How do you optimize #f(x,y)=xy-x^2+e^y# subject to #x-y=8#?

##### 1 Answer

Mar 1, 2016

Minimum of f(x, y) = f(3 ln 2 + 8, 3 ln 2 ).

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#### Explanation:

Substitute x = y + 8.

f(x, y) = g(y) = y(y + 8)

Necessary condition for g(y) to be either a maximum or a minimum is

The second derivative is e^y > 0, for all y. This is the sufficient condition that g(3 ln 2) is the minimum of g(y).