Find the equation of the tangent plane to f(x,y)=x2+3y2f(x, y) = x^2 + 3y^2f(x,y)=x2+3y2 at the point (1,1,4)(1, 1, 4)(1,1,4).
z=2x+6yz = 2x + 6yz=2x+6y
z−4=2(x−1)+6(y−1)z - 4 = 2(x - 1) + 6(y - 1)z−4=2(x−1)+6(y−1)
z=2x+6y+4z = 2x + 6y + 4z=2x+6y+4
z−1=2(x−1)+6(y−1)z - 1 = 2(x - 1) + 6(y - 1)z−1=2(x−1)+6(y−1)