Pre cal word problem help please?

5.The revenue for a symphony concert is given by the equation R(n)= -n^2 + 480n, where n is the number of tickets sold.

a) Determine the number of tickets that will yield maximum revenue.

b) What is the maximum revenue earned?

last question

once again another problem where I think I have the answer, but it seemed too simple to me.

Pre cal word problem help please?mr messed up

R(n) = -n^2 + 480 n

a)

taking the DERIVATIVE

R = -2n + 480

set equaiton to ZERO

0 = -2n + 480

2n = 480

n = 240 ANSWER

b).

SUBSTITUTE into the original equation

R(n) = -n^2 + 480 n

R(n) = -240^2 + 480(240)

R(n) = -57600 + 115200

R(n) = $57600 ANSWER

CHECK

R(n) = -n^2 + 480 n

at n = 200, R(n) = $56000 which is less

at n = 280, R(n) = $56000 which is less

at n = 480, R(n) = $0 which is less

at n = 0, R(n) = $0 which is less

The point used were chosen to show the graph is a parabola with the maximum point at n = 240