申論題

5. (20%) Let z = f(x,y) be a function and fx and fy exist and z= P(x,y) be the tangent plane of z = f(x,y) at (a, b, f(a,b)). Show that P(a+Δx, b+Δy) - P(a, b) = fx(a,b)Δx+fy(a,b)Δy where Δx is the change in x and Δy is the change in y.