Find the number of units that produce a maximum revenue, r =95x-0.1x^2, where r is the total revenue in dollars and x is the number of units sold

units

Step-by-step explanation:

Method 1

The given revenue function is .

We rewrite this function in the vertex form by completing the square.

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We add and subtract half the coefficient of multiplied by a factor of , which is to get,

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We factor out of the first two expressions again to get,

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We now got a perfect square.

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Therefore the maximum revenue occurs when units were sold.

Method 2

Use derivatives to find the x-value of the maximum point.

At maximum point,

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