Use a graphing utility to graph the function and then answer the question.
-The number of mosquitoes $\mathrm { M } ( \mathrm { x } )$, in millions, in a certain area depends on the June rainfall $x$, in inches: $M ( x ) = 4 x - x ^ { 2 }$. What rainfall produces the maximum number of mosquitoes?
A) 16 in.
B) 4 in.
C) 0 in.
D) 2 in.

Question

Quizplus · Accepted Answer

The function $M(x) = 4x - x^2$ is a quadratic function that opens downwards. The maximum value occurs at the vertex, which is at $x = -\frac{b}{2a} = -\frac{4}{2(-1)} = 2$. Thus, 2 inches of rainfall produces the maximum number of mosquitoes.

Use a Graphing Utility to Graph the Function and Then M(x)\mathrm { M } ( \mathrm { x } )M(x)

Use a Graphing Utility to Graph the Function and Then $\mathrm { M } ( \mathrm { x } )$