given z=f(x,y)=x 2 +y 2 /2, g(t)=f(x 0 +th, y 0 +tk), h and k are arbitrary. suppose(x 0, y 0 ) is a point where f(x,y) is minimized.

given z=f(x,y)=x2+y2/2, g(t)=f(x0+th, y0+tk), h and k are arbitrary. suppose(x0,y0) is a point where f(x,y) is minimized. Derive the condition that must be satisfied for f(x0,y0) to be such a minimum. This will involve calculating g(t) for f(x) and then use first and second derivative of g(t) to find the optimal conditions that let you solve for (x0,y0)