The ticket office at Orchestra Center estimates that if it charges x dollars for box seats for a concert, it will sell 50 - x^2 box seats. The function S = 50x - x2 gives the estimated income from the sale of box seats. Graph the function, and use the graph to find the price for box seats that will give the greatest income.
A.$50 per box
B.$20 per box
C.$25 per box
D.$50 per box

Question

The ticket office at Orchestra Center estimates that if it charges x dollars for box seats for a concert, it will sell 50 - x^2 box seats. The function S = 50x - x2 gives the estimated income from the sale of box seats. Graph the function, and use the graph to find the price for box seats that will give the greatest income. 
A.$50 per box 
B.$20 per box 
C.$25 per box
 D.$50 per box

anonymous · Answer

Take the derivative of the function. The derivative gives you the gradient of the curve. Once you have that, equate the derivative to zero and you'll get the answer. This gives the answer because when gradient will equal zero, the change in income will be zero. So the maximum income will be reached when gradient will be zero. You could also do it my plotting the graph.$$50 x - x^2$$
$$dy/dx = 50 - 2x$$$$0 = 50 - 2x$$$$-50 = -2x$$$$x = 25$$ The answer is C.