Question

The number of tickets sold each day for an upcoming performance is given by N(x)=-0.6x^2+13.2x+15, where x is the number of days since the concert was first announced. When will daily ticket sales peak and how many tickets will by sold that day?

Answer 1

First, x>=0 (equal or greater)
dN/dx = N'(x) = -1.2x+13.2
the peak is occuring when N'(x)=0
N'(x)=0 => -1.2x+13.2=0 => x=13.2/1.2 => x=11

So the peak day was day 11.

Now, to find how many ticket where sold, use x=11 in N(x)=-0.6x^2+13.2x+15

The anwser is 87.6 I think.