Solve the problem.
-The number of mosquitoes $M(x)$, in millions, in a certain area depends on the June rainfall $x$, in inches: $\mathrm{M}(\mathrm{x})=4 \mathrm{x}-\mathrm{x}^{2}$. What rainfall produces the maximum number of mosquitoes?
A) 16 inches
B) 4 inches
C) 0 inches
D) 2 inches

Question

Quizplus · Accepted Answer

The function $M(x) = 4x - x^2$ is a quadratic equation in the form of $ax^2 + bx + c$, where $a = -1$, $b = 4$, and $c = 0$. The maximum value of a quadratic function occurs at $x = -\frac{b}{2a}$. Substituting the values, we get $x = -\frac{4}{2(-1)} = 2$ inches.

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

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