Find the difference quotient of $LaTeX: \displaystyle f(x)=6 x + 2$ .

The difference quotient is $LaTeX: \displaystyle \frac{f(x+h)-f(x)}{h}$ . Evaluating $LaTeX: \displaystyle f(x+h)=6 h + 6 x + 2$ and expanding gives $LaTeX: \displaystyle f(x+h)=6 h + 6 x + 2$ Evaluating the difference quotient gives $LaTeX: \displaystyle \frac{(6 h + 6 x + 2)-(6 x + 2)}{h}$ Simplifying gives $LaTeX: \displaystyle \frac{6 h}{h}=6$