Question

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Quadratic word problems (factored...
The number of mosquitoes in Brooklyn (in
millions of mosquitoes) as a function of
rainfall (in centimeters) is modeled by
m(x) = -x(x – 4)
What amount of rainfall results in the
maximum number of mosquitoes?
centimeters

Answer 1

2cm of Rainfall

Explanation:

When the no. of mosquitoes is the highest the slope of graph will be zero

so if we differentiate this function and equate to zero we can find the rainfall amount that gives maximum number of mosquitoes in centimetres.

m(x)= -x²+4x

differentiate

d(x)/d(m(x))= -2x+4

equate to zero

-2x+4=0

2x=4

x=2

answer: 2 cm of rain