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.)
Let x be the salary earned in thousands and the take-home pay = T ......so we have....
T = x - (x/100)(x) = -x^2 / 100 + x
The salary that maximizes the take-home pay is -1 / [ 2 * (-1/100) ] = 100/2 = 50 ⇒ $50,000
[ The take-home pay = $25,000 ]
+1242 
