Question

the rate of change in sales of bicycles at ted's bicycle shop for the year 2001 is given by s(x)=x+7.5, where x represents the month number in 2001 (e.i. x=1 is January, x=2 is February, x=12 is December). is the shop sold 28 bicycles in the month of February, find the shop's total sales function, TS(x).

Answer 1

$TS(x)=\int (x+7.5)dx=\frac{1}{2}x^2+7.5x+C.$

$TS(2)=28\to17+C=28\to C=11.$

$TS(x)=\frac{1}{2}x^2+7.5x+11.$