contestada

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, squared, plus, 14, x What is the maximum possible number of mosquitoes?

Respuesta :

MrRoyal

Answer:

The maximum number of mosquitoes is 7

Step-by-step explanation:

Given

[tex]m(x)= x^2 + 14x[/tex]

Required

Determine the maximum number of the function

First, we differentiate the given function w.r.t x

[tex]m'(x) = -2x + 14[/tex]

Then, we equate m'(x) to 0

[tex]0 = -2x + 14[/tex]

Lastly, we solve for x

[tex]0 = -2x + 14[/tex]

Make 2x the subject

[tex]2x = 14[/tex]

Make x the subject

[tex]x = 14/2[/tex]

[tex]x = 7[/tex]

Answer:

49 Million

Step-by-step explanation: