In a certain city the rate of taxation is the following: x% tax is collected for an income of x thousand dollars. What income, in dollars, will yield the greatest take home pay? (Take-home pay is the income minus the tax on that income.)
+36916 x - x/100 *x
-1/100 x^2 + x
Take derivative = 0
-2/100 x +1 = 0
2/100 x = -1
x = 100/2 = 50 So 50 thousand will net take home $25 000.
