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
 
 should be sold 0.75 thousand boombotix speakers to maximize profit