Given function f x y 4x2 6y2 8x 4y 8 find the optimal value of f x y ........

Explanation:

df/dx =8x -8

df/dx  =0

X=1

df/dy  =12y -4

df /dy =0

12y  -4 =0

Y=1/3

Point (1,1/3)

df²/dx² =8 >0  at point(1,1/3)  minima

df²  /dy² =12

optimal minimum value (1,1/3)

f(1,1/3)=4 × 1 +6 ×  1/3²  -8×  1  -4  × 1 +8   

=10/3