Consider the function f(x,y)=(4x-x2)(2y-y2).Find the first- and second-order partial derivatives off.f=fy=f=fxy=fyy=Find and classify all critical points (x,y)of the function. If there are more blanks than critical points, leave the remaining entries blank.There are several critical points tobe listed. List them lexicographically, that isin ascending order byx-coordinates, and for equal x-coordinates in ascending order byy(1,1),(1,10),(2,-1),(2,3)is a correct orderx and y coordinates is(0,0). Classification:The next critical point isClassification:The next critical point isClassification:The next critical point isClassification:The next critical point isClassification:The classifications can be "saddle point, local maximum, local minimum or cannot be determined".