Solve the problem.
-The number of mosquitoes $M ( x )$, in millions, in a certain area depends on the June rainfall $x$, in inches, according to the equation $M ( x ) = 6 x - x ^ { 2 }$. What rainfall produces the maximum number of mosquitoes?
A) 3 in.
B) $6 \mathrm { in. }$
C) $0 \mathrm { in }$.
D) $36 \mathrm { in. }$

Question

Quizplus · Accepted Answer

The maximum value of $M(x)$ occurs at the vertex of the parabola represented by the equation $M(x) = 6x - x^2$. The x-coordinate of the vertex can be found using the formula $-\frac{b}{2a}$ for a quadratic equation in the form $ax^2 + bx + c$. Here, $a = -1$ and $b = 6$, so the x-coordinate is $-\frac{6}{2(-1)} = 3$. This means the maximum number of mosquitoes occurs with 3 inches of rainfall.

Solve the Problem M(x)M ( x )M(x) , in Millions, in a Certain Area Depends on the )

Solve the Problem $M ( x )$ , in Millions, in a Certain Area Depends on the )