접평면 공식은 \displaystyle z - z_0 = f_x(x_0, y_0)(x - x_0) + f_y(x_0, y_0)(y - y_0) 입니다.

1.편도함수:

\displaystyle f_x = 2x,\ f_y = 6y.

2.기울기:

\displaystyle f_x(1,1) = 2,\ f_y(1,1) = 6.

3.방정식:

\displaystyle z - 4 = 2(x - 1) + 6(y - 1)

\displaystyle z - 4 = 2x - 2 + 6y - 6

\displaystyle 2x + 6y - z = 4 - 2 - 6\;\Longrightarrow\;2x + 6y - z = 4