# functions

• February 5th 2013, 11:50 AM
algebra123
functions
Show that if f = f(x,y) and fyy = 0, then f(x,y) = g(x)y + h(x) for some functions g, h.
(Start by stating the form taken by fy.)

There is nothing in our notes to suggest what the significance of fyy=0 has, and even so I don't know where to start. Help please?
• February 5th 2013, 11:59 AM
Plato
Re: functions
Quote:

Originally Posted by algebra123
Show that if f = f(x,y) and fyy = 0, then f(x,y) = g(x)y + h(x) for some functions g, h.
(Start by stating the form taken by fy.)

If $f_{yy}=0$ then it is clear that $f_y=g(x)$ for some $g$.

Hence $f(x,y)=g(x)y+h(x)$ for some $h$.
Here $h(x)$ 'acts' as the constant $C$ in the indefinite anti-derivative.