How to find profit-maximizing solution given inverse demand function and total cost function

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Problem text:
The Inverse Demand Curve A Monopoly Faces Is P= 100 - Q. The Firm's Cost Curve Is C(Q) = 40 +5Q. What Is The Profit-Maximizing solution?

How does your answer change if C(Q) = 100 + 5Q?
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Thank you! One question, if I want to make sure that it was a maximum I found and not a minimum, I would need to check the second order conditions correct? So that would be the derivative of 100 - 2Q, which would just be -2. And since -2 < 0, is is indeed a maximum that we found? Is my logic correct?

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