Calculus Problem?

Note that the values of "a" & "b" are the amount of taxes previously paid on the income.....a =0 & b = 0.12{20000]...and if the tax was 20% on income above 80000, then a "c" value would be [0.12(20,000) + 0.16(60,000)]..etc for the different rates as the income increases...the more you earn the higher the taxes on the increased earnings...