Find the difference quotient of $LaTeX: \displaystyle f(x)=2 - 4 x$ .

The difference quotient is $LaTeX: \displaystyle \frac{f(x+h)-f(x)}{h}$ . Evaluating $LaTeX: \displaystyle f(x+h)=- 4 h - 4 x + 2$ and expanding gives $LaTeX: \displaystyle f(x+h)=- 4 h - 4 x + 2$ Evaluating the difference quotient gives $LaTeX: \displaystyle \frac{(- 4 h - 4 x + 2)-(2 - 4 x)}{h}$ Simplifying gives $LaTeX: \displaystyle \frac{- 4 h}{h}=-4$