Find the difference quotient of $LaTeX: \displaystyle f(x)=7 x^{2} + 10 x + 5$ .

The difference quotient is $LaTeX: \displaystyle \frac{f(x+h)-f(x)}{h}$ . Evaluating $LaTeX: \displaystyle f(x+h)=10 h + 10 x + 7 \left(h + x\right)^{2} + 5$ and expanding gives $LaTeX: \displaystyle f(x+h)=7 h^{2} + 14 h x + 10 h + 7 x^{2} + 10 x + 5$ Evaluating the difference quotient gives $LaTeX: \displaystyle \frac{(7 h^{2} + 14 h x + 10 h + 7 x^{2} + 10 x + 5)-(7 x^{2} + 10 x + 5)}{h}$ Simplifying gives $LaTeX: \displaystyle \frac{7 h^{2} + 14 h x + 10 h}{h}=7 h + 14 x + 10$