Find the difference quotient of $LaTeX: \displaystyle f(x)=- x - 6$ .

The difference quotient is $LaTeX: \displaystyle \frac{f(x+h)-f(x)}{h}$ . Evaluating $LaTeX: \displaystyle f(x+h)=- h - x - 6$ and expanding gives $LaTeX: \displaystyle f(x+h)=- h - x - 6$ Evaluating the difference quotient gives $LaTeX: \displaystyle \frac{(- h - x - 6)-(- x - 6)}{h}$ Simplifying gives $LaTeX: \displaystyle \frac{- h}{h}=-1$