Question

What is the difference quotient for the linear function f(x)=-4x+5

Answer 1

The difference quotient is given by:

`(f(x+h)-f(x))/(h)`

Let's find it:

`\begin{gathered} (\lbrack-4(x+h)+5\rbrack-\lbrack-4x+5\rbrack)/(h)=(\lbrack-4x-4h+5\rbrack-\lbrack-4x+5\rbrack)/(h) \\ =(-4x-4h+5+4x-5)/(h) \\ =(-4h)/(h) \\ =-4 \end{gathered}`

Therefore, the difference quotient for the function given is -4