Find the difference quotient of $LaTeX: \displaystyle f(x)=3 x + 3$ .

The difference quotient is $LaTeX: \displaystyle \frac{f(x+h)-f(x)}{h}$ . Evaluating $LaTeX: \displaystyle f(x+h)=3 h + 3 x + 3$ and expanding gives $LaTeX: \displaystyle f(x+h)=3 h + 3 x + 3$ Evaluating the difference quotient gives $LaTeX: \displaystyle \frac{(3 h + 3 x + 3)-(3 x + 3)}{h}$ Simplifying gives $LaTeX: \displaystyle \frac{3 h}{h}=3$