Solve the problem.
-The number of mosquitoes $\mathrm { M } ( \mathrm { x } )$, in millions, in a certain area depends on the June rainfall $x$, in inches: $\mathrm { M } ( \mathrm { x } ) =$ $14 x - x ^ { 2 }$. What rainfall produces the maximum number of mosquitoes?
A) $0 \mathrm { in }$.
B) $14 \mathrm { in. }$
C) $196 \mathrm { in } .$
D) $7 \mathrm { in }$.

Question

Quizplus · Accepted Answer

The maximum value of a quadratic function $f(x) = ax^2 + bx + c$ occurs at $x = -\frac{b}{2a}$. For $M(x) = -x^2 + 14x$, $a = -1$ and $b = 14$, so the maximum occurs at $x = -\frac{14}{2(-1)} = 7$.

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

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