Yesterday, Integrated Learning posted a 700 level GMAT question on our blog. Today, they have followed up with the answer:
This is the only advanced algebra you’ll need on the test. It’s not the only way to solve it, but it’s the easiest way to solve it.
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. That’s the max or min.
In this case we are given
P = -25×2 + 7500x
To find the derivative, multiply each number by the exponent it’s connected to, and subtract the exponent by 1. Here, that will look like:
P’ = -50x + 7500
Set P’ to zero, and solve:
0 = -50x + 7500
50x = 7500
x = 150
If you’re not sure this really worked, try plugging in numbers, or even running the original equation in Excel. You will see that at x = 150, P is the maximum it can be.
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