Word problem help please!

Question

The manufacturer of a CD player has found that the revenue R (in dollars) is R(p) = -4p2 + 1440p, when the unit price is p dollars. If the manufacturer sets the price p to maximize revenue, what is the maximum revenue to the nearest whole dollar?

Answer 1

Take the 1st derivative to get local extrema. -8p+1440 set it equal to zero and solve for p

8p=1440 p=180 Answer $180 price to maximize revenue

But maybe you don't know calculus or derivatives

The revenue equation is a parabola, opening downward, with price zero generating zero revenues.

Set the revenue = 0, solve for p to get -4p² + 1440p = 0 factor into

(-4)p(p-360)=0 or p=0, p=360 setting each factor = 0

But we want the midpoint, the price half way between the 2 zero revenue generating prices, because parabolas are symmetric at the midpoint between any two equal x values generating the same y value.

we want 360+0 all divided by 2 or 360/2=180 $180 is the maximum revenue generating price.

If you get the same answer working it 2 different ways, odds are good it's correct.