Your picture has several issues.
- x is not defined. It appears to be the number of apartments rented.
- R(x) is defined two different ways. The first way, it looks like it is the revenue from a single apartment. The second way, it looks like it is the revenue from the entire apartment complex.
- The derivative is in error. It should be -20x +2000. In any event, this is not the derivative you want. You're not trying to maximize revenue; you're trying to maximize profit.
- It might be useful to write an equation for profit: P(x) = R(x) -200x = -10x² +1800x. Then when you go to maximize it, your derivative will be P'(x) = 0 = -20x +1800 ⇒ x = 90.
Your answer is correct, but the path you followed to get there has a few potholes.
The answer to this problem is 745.
149 * 5 = 745
In the future, you can do this with a calculator.
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I can't see the picture right, it's backward sorry
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edit the picture and take a better one
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the answer should be 5/16