# The number of mosquitoes M(x), in millions, in a certain area depends on the June rainfall x, in inches, and is represented by the equation M(x)=19x-x^2.What's rainfall produces the maximum number of mosquitoes?

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The number of mosquitoes M(x), in millions, in a certain area depends on the June rainfall x, in inches, and is represented by the equation M(x)=19x-x^2.What's rainfall produces the maximum number of mosquitoes?

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Step 1

According to the given question,

Let x be the June rainfall in inches

And M(x) is the number of mosquitoes in millions.

And M(x) is given by:

Step 2

To calculate the maximum number of mosquitoes apply second derivative test.

So first...

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### Algebra 