Classify the critical point (1,$\frac{\pi}{2}$,0) of the function $f(x,y,z) = xsinz-zsiny$
I found the Hessian matrix but it had a zero determinant.
I tried looking at how the function behaves when setting z to different for values for instance:
When $z = y$ I get the function $f(x,y,y) = sin(y)(y-x)$ which I dont think is handy to me.
I have struggled to find many examples involving three variables and feel like I'm getting no where.
If anyone could help set me in the right direction I would really appreciate it.