Find the difference quotient of $LaTeX: \displaystyle f(x)=4 x + 3$ .

The difference quotient is $LaTeX: \displaystyle \frac{f(x+h)-f(x)}{h}$ . Evaluating $LaTeX: \displaystyle f(x+h)=4 h + 4 x + 3$ and expanding gives $LaTeX: \displaystyle f(x+h)=4 h + 4 x + 3$ Evaluating the difference quotient gives $LaTeX: \displaystyle \frac{(4 h + 4 x + 3)-(4 x + 3)}{h}$ Simplifying gives $LaTeX: \displaystyle \frac{4 h}{h}=4$