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