Chapter 13, Problem 67RE

Using a Function In Exercises 67 and 68, (a) find the gradient of the function at P, (b) find a unit normal vector to the level curve $f(x,y)=c$ at P, (c) find the tangent line to the level curve $f(x,y)=c$ at P, and (d) sketch the level curve, the unit normal vector, and the tangent line in the xy -plane.

$\begin{array}{l}f(x,y)=9x^2-4y^2\\ c=65,P(3,2)\end{array}$