Find the linearization L(x,y) of the function f(x,y)=

Find the linearization L(x,y) of the function f(x,y)= sqrt(80-16x^2-4y^2) at (2,0)

f(2, 0) = 4

f_x = (1/2) (80 - 16x^2 - 4y^2)^(-1/2) * -32x ==> f_x (2, 0) = -32/4 = -8
f_y = (1/2) (80 - 16x^2 - 4y^2)^(-1/2) * -8y ==> f_y (2, 0) = 0

So, L(x, y) = 4 - 8(x - 2) + 0(y - 0).

I hope this helps!