Need Help Related to Maximum Revenue

[sandi2001]

The demand function for a product is modeled by p(x) = 50e^(−0.0000125x) where p is the price per unit in dollars and x is the number of units. What price will yield a maximum revenue?

Can you guys help a student out? I'm struggling with the new normal and there are no profs available to consult with.

 

[tkhunny]

Did you use the hint?
Does "maximum" sound like it might be an application of a Derivative?

 

[JeffM]

How would you express that verbal hint mathematically? You cannot use mathematics until you express things in the language of mathematics.

 

[HallsofIvy]

The hint tells you that if you sell "x" items at price "p" each then your revenue is "px". You are told that \(\displaystyle p(x) = 50e^(−0.0000125x)\) so the revenue is \(\displaystyle px= 50xe^{-0.0000125x}\). Differentiate that using the "product rule".

 

[sandi2001]

Thank you very much for the clarifications, good sirs.