Find the critical point of the function f(x,y)=−(36x+6y^2+ln(|x+y|)) . Use the Second Derivative Test to determine whether it is a local min, max, saddle point or test fails

Question

Find the critical point of the function f(x,y)=−(36x+6y^2+ln(|x+y|)) .

Use the Second Derivative Test to determine whether it is a local min, max, saddle point or test fails

Answer 1

critical points exist where f_x & f_y=0

f_x=-36-1/(x+y) =0 ... 1/(x+y)=-36

f_y=-12y -1/(x+y) =0 ... y= 3 and x= -109/36

fxx=0 fyy=-12 fxy=0 thus D=0*-12-0²=0 ... indeterminate