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 equation $\mathrm { M } ( \mathrm { x } ) = 9 \mathrm { x } - \mathrm { x } ^ { 2 }$. What rainfall produces the maximum number of mosquitoes?
A) $0 \mathrm { in }$.
B) $9 \mathrm { in }$.
C) $4.5 \mathrm { in }$.
D) $81 \mathrm { in }$.

Question

Quizplus · Accepted Answer

The maximum value of a quadratic function $f(x) = ax^2 + bx + c$ occurs at $x = -\frac{b}{2a}$. For $M(x) = -x^2 + 9x$, $a = -1$ and $b = 9$, so the maximum occurs at $x = -\frac{9}{2(-1)} = 4.5$.

Solve the Problem -The Number of Mosquitoes M(x)\mathrm { M } ( \mathrm { x } )M(x)

Solve the Problem
-The Number of Mosquitoes $\mathrm { M } ( \mathrm { x } )$