Question

The point (0,0) in the domain of f(x, y) = sin(xy) +20 is a point of​

Answer 1

Answer:

The point (0,0) in the domain of f(x, y) = sin(xy) +20 is a point of​ Saddle point

Step-by-step explanation:

Given f(x,y) = sin(xy) + 20

fxx = -y^2sin(xy)

fyy = -x^2sin(xy)

fxy= cos(xy)-xysin(xy)

Now,

fxx.fyy - (fxy)^2 = (xysin(xy))^2 - (xysin(xy))^2 - cos(xy)^2 +2xycos(xy)sin(xy)

                        = 2xycos(xy)sin(xy)- cos(xy)^2

Now, fxx.fyy - (fxy)^2 at (0,0) = -1

So, fxx.fyy - (fxy)^2 < 0

So its a saddle point.