Chapter 13.6, Problem 45E

(a)

To determine

To calculate: $f\left(x,y\right)=3x^2-2y^2$, $P\left(1,1\right)$ is given, find the gradient of the given function at P

(b)

To determine

To calculate: $f\left(x,y\right)=3x^2-2y^2$, $\nabla f\left(1,1\right)=6\text{i}-4\text{j}$, $c=1$.

Is given, find unit normal vector to the level curve $f\left(x,y\right)=c$ at $P$

(c)

To determine

To calculate: ,$f_x\left(x,y\right)=6x$, $f_y\left(x,y\right)=-4y$, $P\left(1,1\right)$ is given, findtangent line to the level curve $f\left(x,y\right)=3x^2-2y^2-1$ at $P\left(1,1\right)$

(d)

To determine

To graph: The curve, $f\left(x,y\right)=3x^2-2y^2-1$, and the point $P\left(1,1\right)$.

is given, find the level curve, the unit normal vector, and the tangent line in the x y-plane.