The number of speakers that should be sold to maximize profit is 0.9
Vertex of a quadratic equation
Given the function that represents the profit made in selling x thousand Boombotix speakers expressed as:
P(x)=6+9x−5x^2
In order to maximize the profit, p'(x) = 0, hence;
P'(x) =9 - 10x
0 = 9 - 10x
x = 9/10
Hence the number of speakers that should be sold to maximize profit is 0.9
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