Calculus 3 Tangent

Question

Find the linear approximation to the equation f(x,y)=4xy−2xy^2 at the point (2,1,4), and use it to approximate f(2.2,1.1)

Answer 1

f_x = 4y - 2y² ; f_y = 4x - 4xy

f_x | _(2,1) = 2 ; f_y | _(2,1) = 0

L(x,y) = 4 + 2(x - 2) + 0(y - 1)

L(2.2 , 1.1) = 4.4