SOLUTION: Find the number of units x that produces a maximum revenue R in the given equation. R = 36x^2/3 – 2x

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Question 426063: Find the number of units x that produces a maximum revenue R in the given equation.
R = 36x^2/3 – 2x
Answer by htmentor(1343) About Me  (Show Source):
You can put this solution on YOUR website!
We have the function R = 36x^(2/3) – 2x
The function is maximized at the point where the derivative is equal to 0.
dR/dx = 0 = (2/3)36x^(-1/3) - 2.
Solving for x we get
12x^(-1/3) = 1 -> x^(1/3) = 12 -> x = 12^3 = 1728
So the answer is 1728 units.
The graph looks like this:
graph%28300%2C200%2C-200%2C2000%2C-200%2C2000%2C36x%5E%282%2F3%29-2x%29