Step 1 :The problem is asking for the maximum point of the quadratic function \(N(x)=-0.4 x^{2}+9.6 x+13\). This is a parabola that opens downwards because the coefficient of \(x^2\) is negative.
Step 2 :The maximum point of a parabola \(y=ax^2+bx+c\) is given by \(x=-\frac{b}{2a}\). We can use this formula to find the day when the ticket sales will peak.
Step 3 :After finding the value of \(x\), we can substitute it back into the function to find the number of tickets sold that day.
Step 4 :By solving, we find that \(x = 12\), which means the ticket sales will peak on the 12th day after the concert was first announced.
Step 5 :Substituting \(x = 12\) back into the function, we find that \(N = 70.6\), which means approximately 71 tickets will be sold that day (since we can't sell a fraction of a ticket).
Step 6 :So, the final answer is \(\boxed{12, 71}\). The daily ticket sales will peak on the 12th day after the concert was first announced, and the number of tickets sold that day will be approximately 71.