Find the difference quotient of $LaTeX: \displaystyle f(x)=9 - x$ .

The difference quotient is $LaTeX: \displaystyle \frac{f(x+h)-f(x)}{h}$ . Evaluating $LaTeX: \displaystyle f(x+h)=- h - x + 9$ and expanding gives $LaTeX: \displaystyle f(x+h)=- h - x + 9$ Evaluating the difference quotient gives $LaTeX: \displaystyle \frac{(- h - x + 9)-(9 - x)}{h}$ Simplifying gives $LaTeX: \displaystyle \frac{- h}{h}=-1$