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