How do i find the "local extrema" for a function like this: f(x,y) = xy+y-15x

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- November 25th 2009, 06:43 AMsquareLocal Extrema help
How do i find the "local extrema" for a function like this: f(x,y) = xy+y-15x

- November 25th 2009, 07:04 AMSoroban
Hello, square!

Quote:

How do i find the "local extrema" for a function like this: .

And test the critical value(s) in: .

If all this is meaningless to you,

. . (1) you should not have been assigned this problem, or

. . (2) you weren't paying attention in class.

- November 25th 2009, 07:15 AMtonio

Solve the equations , and then use the Hessian's determinant in the points that you found above, : if this determinant is positive and (1) , then the point you found is a local minimum, and if (2) the point is then a local maximum .

If the determinant is negative then the point is a saddle point (not max. not min.), and if the determinant is zero then the Hessian matrix's test fails to decide.

Tonio