Problem

A product's revenue is modeled by \(R(p)~=~-(p~-~10)^2~+~100\), where \(p\) is the price in dollars. Interpret when the revenue is increasing and when it is decreasing as the price changes.

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Revenue increases as the price rises to 10 dollars, and it decreases when the price goes above 10 dollars because the graph reaches its maximum at p = 10.

Revenue decreases as the price rises to 10 dollars, and it increases when the price goes above 10 dollars because the coefficient of the squared term is negative.

Revenue increases until the price reaches 100 dollars, and it decreases after that because 100 is the key value shown in the equation.

Revenue increases as the price moves away from 10 dollars on either side, and it decreases only exactly at 10 dollars because that is the turning point.

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A product's revenue is modeled by \(R(p)~=~-(p~-~10)^2~+~100\), where \(p\) is the price in dollars. Interpret when the revenue is increasing and when it is decreasing as the price changes.

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