Suppose a product's profit function is given by $\displaystyle \pi{\left({q}\right)}=-{8}{q}^{{2}}+{500}{q}$, where $\displaystyle \pi{\left({q}\right)}$ is in dollars and $\displaystyle {q}$ is the number of units sold. (Economists use the symbol $\displaystyle \pi$ to represent profit since $\displaystyle {p}$ is usually used for price. In this context, $\displaystyle \pi$ does not represent the number $\displaystyle \pi\approx{3.14159}$.)

Use the marginal profit function to find the approximate profit generated by selling the $\displaystyle {35}^{{{t}{h}}}$ unit.
Marginal profit$\displaystyle =$ Preview Question 6   dollars per unit