How can you maximize your happiness under a budget? When does a function reach its minimum value? When does a curve change direction? The calculus of extrema explains these "extreme" situations.

A shop sells \(500\) smartphones a week for \($450\) each. A market survey shows that each decrease of \($5\) on the price will result in the sale of an additional \(10\) smartphones per week. What price of the smartphone would result in maximum revenue?

**Details and assumptions**

The revenue is defined as the product of the number of items sold and the price of each item.

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