SOLUTION: The number of mosquitoes M(x), in millions, in a certain area depends on the June rainfall x, in inches,according to the functions M(x) =19x-x^2.What rainfall produces the maximum

Question 721213: The number of mosquitoes M(x), in millions, in a certain area depends on the June rainfall x, in inches,according to the functions M(x) =19x-x^2.What rainfall produces the maximum number of mosquitoes?
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
M(x) =19x-x^2
since the coefficient associated with the x^2 is NEGATIVE we know it is a parabola that opens downwards. Therefore, the vertex is the maximum.
x-value of vertex:
x = -b/(2a)
x = -19/(2(-1))
x = -19/(-2)
x = 9.5 inches (answer)
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