Question

Find the difference quotient of f(x)=5x+4

Answer 1

the differnce quotient is basically taking the derivitive (result will be f'(x)=5, but anyway)

here is the disffernce quotient

`lim_(h\rightarrow0)(f(x+h)-f(x))/(h)`

so
for your equation

`lim_(h\rightarrow0)((5(x+h)+4)-(5x+4))/(h)`

`lim_(h\rightarrow0)(5x+5h+4-5x-4)/(h)`

`lim_(h\rightarrow0)(5h)/(h)`
h's cancel and you are left with 5
the differnce quotient is 5