Question

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?

Answer 1

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