Homework SourseFind all critical points of the function fxy 16y 13x3 xy4
Find all critical points of the function f(x,y) = 16y - (1/3(x^3)) - x(y^4) +5.
Indicate whether each such point gives a local maximum, a local minimum, or whether it is a saddle point.
Indicate whether each such point gives a local maximum, a local minimum, or whether it is a saddle point.
Solution
df/dx=-x^2-y^4=0 df/dy=16-4xy^3=0 -x^2=y^4 xy^3=4 -x^2=y^4 is not possible except when x=y=0 but x=y=0 does not satisfy xy^3=4 So there are no critical points
