Given function f x y 3x2 4y2 4x 4y 4 the optimal value of f x y would be ........

Mathematics (NDA) Diffrentiation

Given function f(x,y) =3x² +4y² -4x -4y +4 ,the optimal value of f(x,y) would be?

2/3

5/3

9/2

11/3

f(x,y) =3x² +4y² -4x -4y +4

df/dx =6x -4

let df/dx =0

X=4/6

df/dy =8y -4

let df /dy =0

8y -4 =0

Y=1/2

Point (2/3,1/2)

df²/dx² =6 >0 at point(2/3,1/2) minima

df² /dy² =8

optimal minimum value (2/3,1/2)

f(1,1/3)=3 × (2/3)² +4 × 1/2² -4× 2/3 -4 × 1/2 +4

=4/3 +1 -8/3-2+4

=5/3

Submit Error