Find an equation of the tangent plane to the surface x² + 2y² + 3z² = 6 at the point(1, 1, 1). A) x + y + z = 3 B) x + 4y + 9z = 14 C) x + 2y + 3z = 6 D) 3x + 2y + z = 6 E) x + 2y - 3z = 6

Question

Quizplus · Accepted Answer

The gradient of the surface at (1, 1, 1) is (2x, 4y, 6z). At (1, 1, 1), this is (2, 4, 6). The equation of the tangent plane is 2(x-1) + 4(y-1) + 6(z-1) = 0, which simplifies to x + 2y + 3z = 6.

Find an Equation of the Tangent Plane to the Surface