Question

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?

Answer 1

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

 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:
 7 centimeters of rain will produce the maximum number of mosquitoes.