If p ( x ) = 8 + 6 x − 4 x 2 p(x)=8+6x-4x2 represents the profit in selling x x thousand boombotix speakers, how many speakers should be sold to maximize profit?
For this case we have the following equation: p (x) = 8 + 6x-4x2 We must derive the equation to find the maximum of the function. We have then: p '(x) = 6-8x We match zero: 6-8x = 0 We clear x: 8x = 6 x = 6/8 x = 3/4 x = 0.75 speakers Answer: should be sold 0.75 thousand boombotix speakers to maximize profit
