Find all three critical points for the function: f(x,y)=x 2
y−xy+3y 2
. Classify each point is a local max, local min, or saddle point. An object is traveling along the line y=2x+1 heading up and to the right. If the temperature at (x,y) in degrees celsius is given by f(x,y)=x 2
y+x−y, and if the plane is measured in meters, what is the instantaneous temperature change the object is experiencing at the instant when x=3 ? Suppose z=xcos(xy). Suppose further that x=e st
and y=st. Find ∂s
∂z
​
at s=2 and t=1. You do not need to provide your final answer in numeric form (leaving unevaluated sines and cosines is fine).