the differnce quotient is basically taking the derivitive (result will be f'(x)=5, but anyway)
here is the disffernce quotient
[tex]lim_{h\rightarrow0}\frac{f(x+h)-f(x)}{h}[/tex]
so
for your equation
[tex]lim_{h\rightarrow0}\frac{(5(x+h)+4)-(5x+4)}{h}[/tex]
[tex]lim_{h\rightarrow0}\frac{5x+5h+4-5x-4}{h}[/tex]
[tex]lim_{h\rightarrow0}\frac{5h}{h}[/tex]
h's cancel and you are left with 5
the differnce quotient is 5
