Chapter 14.3, Problem 105E

To determine

To find:

To graph given function

To determine

(b)

To find:

$f_x\left(x,y\right)$, $f_y\left(x,y\right)$ when $\left(x,y\right)\ne \left(\mathrm{0,0}\right)$

To determine

(c)

To find:

$f_x\left(\mathrm{0,0}\right)$, $f_y\left(\mathrm{0,0}\right)$

To determine

(d)

To show:

$f_{xy}\left(\mathrm{0,0}\right)=-1$ and $f_{yx}\left(\mathrm{0,0}\right)=1$

To determine

(e)

To show:

Does $f_{xy}\left(\mathrm{0,0}\right)=-1$ $f_{yx}\left(\mathrm{0,0}\right)=1$ contradicts Clairaut’s Theorem using graph.