I was wondering if I did the following problem right:
Write the equation of the plane tangent to the given surface at the given point P.
xyz+ 2x^3 - y^2 + z^2 = 10; P(2, -1, -1)
So what I did was find the gradient of the above and got:
<yz + 4x, xz - 2y, xy - 2z>
Substituting P in I got, a normal vector of <9, 0, 0>
This led to a plane equation of:
9(x - 2) = 0