Determine the equation of the tangent plane to 2𝑥^2+𝑦^2+5𝑧^2=26 at the point (−1,2,2).

Answer 1

The gradient is (4x, 2y, 10z), which is at (-1, 2, 2) is (-4, 4, 20)

Then, the tangent plane is -4x + 4y + 20z = (-4*-1+2*4+2*20) = 52, or

-x + y + 5z = 13