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malfutka [58]
2 years ago
15

The number of mosquitoes in anchorage, alaska (in millions of mosquitoes) as a function of rainfall (in centimeters) is modeled

by: m(x)=-x^2+14xm(x)=−x 2 +14xm, left parenthesis, x, right parenthesis, equals, minus, x, start superscript, 2, end superscript, plus, 14, x how many centimeters of rain will produce the maximum number of mosquitoes?
Mathematics
1 answer:
bekas [8.4K]2 years ago
3 0
M (x) = - x ^ 2 + 14x
 To find the maximum function, the first thing to do is to obtain the first derivative:
 m '(x) = - 2x + 14
 We match zero:
 0 = -2x + 14
 We clear x:
 x = 14/2 = 7
 x = 7
<span>
 We verify that this value is a maximum through the second derivative:
 m '' (x) = - 2
 m '' (7) = - 2 (<0 therefore it is a maximum)

 Answer:
<span> 7 centimeters of rain will produce the maximum number of mosquitoes.</span></span>
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