Chapter 13, Problem 68RE

Using a FunctionIn 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.

$\begin{array}{l}f(x,y)=4y\sin x-y\\ c=3,P\left(\frac{\pi }{2},1\right)\end{array}$