Solve the problem.
-The number of mosquitoes $\mathrm { M } ( \mathrm { x } )$, in millions, in a certain area depends on the June rainfall $\mathrm { x }$, in inches, according to the function $\mathrm { M } ( \mathrm { x } ) = 20 \mathrm { x } - \mathrm { x } ^ { 2 }$. What rainfall produces the maximum number of mosquitoes?
A) 20 in.
B) 400 in.
C) 0 in.
D) 10 in.

Question

Quizplus · Accepted Answer

To find the rainfall that produces the maximum number of mosquitoes, we need to find the maximum value of the function M(x) = 20x - x^2. To do this, we can take the derivative of M(x) with respect to x, set it equal to 0, and solve for x.

M'(x) = 20 - 2x = 0

Solving for x, we get x = 10.

So the maximum value of M(x) occurs at x = 10, which is 200 million mosquitoes. Therefore, the answer is D) 10 in.

Solve the Problem M(x)\mathrm { M } ( \mathrm { x } )M(x)

Solve the Problem $\mathrm { M } ( \mathrm { x } )$