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GMAT Problem Solving (PS) | In a certain company, the formula for maximizing profits is

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wcgc wrote:

In a certain company, the formula for maximizing profits is P = -25x^2 + 7500x,, where P is profit and x is the number of machines the company operates in its factory. What value for x will maximize P?

A) 10
B) 50
C) 150
D) 200
E) 300

This one is from IntegratedLearning.

Here's what I did:
[Reveal] Spoiler:
P=-25x2+7500X => P=-50+7500X, to max. P, we need to max X. So I picked E, why isn't that correct?

The OA states: To find a maximum or minimum value of an equation with an exponent in it, you take the derivative of the equation, set it to zero, and solve. I don't really get what that means. So whoever solves it, could you plz post explanation of what the above sentence mean as well?


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