Chapter 13, Problem 51RE

(a)

To determine

To calculate: The gradient of the function $f\left(x,y\right)=9x^2-4y^2$ at the point $P\left(3,2\right)$.

(b)

To determine

To calculate: A unit normal vector for the level curve of the function $f\left(x,y\right)=9x^2-4y^2$ at the point $P\left(3,2\right)$ where $c=65$.

(c)

To determine

To calculate: The line tangent to the level surface $9x^2-4y^2=c$ at the point $P\left(3,2\right)$ where c is 65.

(d)

To determine

To graph: The tangent line, the normal vector and the level curve.