How is fxy = 1 found for finding local extreme values?

[bobsmith76]

Homework Statement

see attachment

The Attempt at a Solution

I don't understand how they found f_xy = 1

I understand how they found f_xx, they used simultaneous equations, but I don't understand that notation.

 

[LCKurtz]

Homework Statement

see attachment

The Attempt at a Solution

I don't understand how they found f_xy = 1

I understand how they found f_xx, they used simultaneous equations, but I don't understand that notation.

They didn't find $f_{xx}$ by using simultaneous equations. They just differentiated $f$ twice with respect to $x$. Then to get $f_{xy}$ they differentiated $f_x$ with respect to $y$.

 

[bobsmith76]

Thanks, that makes sense.