Homework SourseWhat are the critical points of fxyx2xyy2ySolution xy x2 2x
What are the critical points of f(x,y)=x^2+xy+y^2+y
Solution
(x,y)= -x^2 + 2xy + y^2 + 2y fx(x,y) = -2x + 2y fy(x,y) = 2x + 2y + 2 -2x +2y = 0 2x + 2y + 2 = 0 I\'m going to factor out the twos and divide them out of the equation y - x = 0 y + x + 1 = 0 y - x = 0 -> y=x and substitute in the other equation y + (y) + 1 = 0 y = -1/2 plug back in a solve for x x = -1/2 so the critical point is (-1/2 , -1/2).![What are the critical points of f(x,y)=x^2+xy+y^2+ySolution (x,y)= -x^2 + 2xy + y^2 + 2y fx(x,y) = -2x + 2y fy(x,y) = 2x + 2y + 2 -2x +2y = 0 2x + 2y + 2 = 0 I\](/WebImages/36/what-are-the-critical-points-of-fxyx2xyy2ysolution-xy-x2-2x-1109167-1761587688-0.webp "What are the critical points of f(x,y)=x^2+xy+y^2+ySolution (x,y)= -x^2 + 2xy + y^2 + 2y fx(x,y) = -2x + 2y fy(x,y) = 2x + 2y + 2 -2x +2y = 0 2x + 2y + 2 = 0 I\")
