The function, $\displaystyle {I}{\left({p}\right)}={1067}{p}^{{2}}+{6670}{p}+{31300},$ gives the amount of annual income a retiree can expect to receive in 30 years, assuming a return on the investment of $\displaystyle {p}$ percent per year.

(Caution: $\displaystyle {p}$ is not to be converted to decimals in this problem. For example, to compute the retirement income for 3.5%, you would compute $\displaystyle {I}{\left({3.5}\right)},$ not $\displaystyle {I}{\left({.035}\right)}$.)

A) Find the marginal change of $\displaystyle {I}$ at $\displaystyle {p}={10.4}$ percent.

Answer: dollars per percent of return.
(Round to 2 decimal places if necessary.)

B) Find the percentage, $\displaystyle {p},$ when the marginal change of $\displaystyle {I}$ is $\displaystyle {25449.2}$ dollars per percent of return.

Answer: percent
(Round to 1 decimal place if necessary.)