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Question
Find the maximum profit that a company can make, if the profit function is given by p(x) = 41 − 72x − 18x2.
Solution
We have p(x) = 41 - 72x - 18x2
p'(x) = -72 - 36x
Now for critical points, p'(x) = 0
-72 - 36x = 0
x = -2
p'' (x) = -36 < 0
∴ Profit is maximum at x = -2, and maximum profit is p(-2) = 41 - 72 (-2) - 18 (-2)2
= 41 + 144 - 72
= 185 - 72
= 133
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