Question

find the maximum and minimum values​

Answer 1

Hey mate, it's already solved. Ask it's own question, I'll answer to it.

Answer 2

Answer:

Step-by-step explanation:

it is very easy question

x^3y^2(1-x-y)

x^3y^2-x^4y^2-x^3y^3

let d(a,b)=fxx*fyy-(fxy)^2

first lets find fx,fxx,fy,fyy and fxy

by question f(x,y)=x^3y^2-x^4y^2-x^3y^3

differentiating first one by x we get

fx=3x^2(y^2)-4x^3(y^2)-3x^2(y^3)

fy=x^3(2y)-x^4(2y)-x^3(3y^2)

fxx=6x(y^2)-12x^2(y^2)-6x(y^3)

fyy=x^3(2)-x^4(2)-x^3(6y)

fxy=3x^2(2y)-4x^3(2y)-3x^2(3y^2)

put fx=0 anf fy=0

and you will get x and y values

substitute in d(a,b)

if d(a,b)>0 and fxx>0 then it is local minima

d(a,b)>0 and fxx<0 then it is local maxima

if d(a,b)<0 it is neither maxima nor minima means it is saddle or point of inflection