Chapter 12.6, Problem 71E

Looking ahead—tangent planes Consider the following surfaces f(x, y, z) = 0, which may be regarded as a level surface of the function w = f(x, y z). A point P(a. b, c) on the surface is also given.

1. a. Find the (three-dimensional) gradient off and evaluate it at P
2. b. The set of all vectors orthogonal to the gradient with their tails at P form a plane. Find an equation of that plane (soon to be called the tangent plane).

71.     $f\left(x,y,z\right)=x^2+y^2+z^2-3=0;P\left(1,1,1\right)$