The number of units is 3000 and the profit is $89500 if the profits from their business with the function P(x)= -0.01x²+60x-500, where x is the number of units they sell and P is the profit in dollars.
What are maxima and minima?
Maxima and minima of a function are the extreme within the range, in other words, the maximum value of a function at a certain point is called maxima and the minimum value of a function at a certain point is called minima.
We are assuming the function is:
P(x) = - 0.01x²+60x-500
P'(x) = -0.02x + 60
P'(x) = 0
x = 3000
P''(x) = 0.02
P''(x) > 0 for all x
The function is maximum at x = 3000
Plug x = 3000 in the function;
P(3000) = $89500
Thus, the number of units is 3000 and the profit is $89500 if the profits from their business with the function P(x)= -0.01x²+60x-500, where x is the number of units they sell and P is the profit in dollars.
Learn more about the maxima and minima here:
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