Homework SourseThe function fxyxy25x28y2has three critical points Enter the
The function f(x,y)=xy^2-5x^2-8y^2has three critical points. Enter them in order of increasing y-coordinate and classify each as a local minimum, local maximum, or saddle point.
First point? type?
Second point? type?
Third point? type?
First point? type?
Second point? type?
Third point? type?
Solution
f\'x = y2 -10x = 0
f\'y = 2xy -16y = 0
or, x=0, y=0
x = 8, so, y = 45
these are the critical points
