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: $\mathrm { M } ( \mathrm { x } ) = 13 \mathrm { x } - \mathrm { x } ^ { 2 }$. What rainfall produces the maximum number of mosquitoes?
A) 0 in.
B) $169 \mathrm { in }$.
C) $6.5 \mathrm { in }$.
D) 13 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 $M(x) = -x^2 + 13x$, $a = -1$ and $b = 13$, so the maximum occurs at $x = -\frac{13}{2(-1)} = 6.5$.

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

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