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

Question

Quizplus · Accepted Answer

The function $M(x) = 6x - x^2$ is a quadratic equation in the form of $ax^2 + bx + c$, where $a = -1$, $b = 6$, and $c = 0$. The vertex of a parabola given by a quadratic equation $ax^2 + bx + c$ is found using the formula $x = -\frac{b}{2a}$. Substituting $a = -1$ and $b = 6$ into the formula gives $x = -\frac{6}{2(-1)} = 3$. Therefore, the rainfall that produces the maximum number of mosquitoes is 3 inches.

The Number of Mosquitoes M(x)M(x)M(x) , in Millions, in a Certain Area Depends on the Certain

The Number of Mosquitoes $M(x)$ , in Millions, in a Certain Area Depends on the Certain