Question

The number of​ mosquitoes, m(x), in​ millions, in a certain area depends on the june​ rainfall, x, in inches. the function that models that phenomenon is upper m left parenthesis x right parenthesis equals 26 x minus x squared .m(x)=26x−x2. find the amount of rainfall that will maximize the number of mosquitoes. what is the maximum number of​ mosquitoes?

Answer 1

2 centimeters will maximize the number of mosquitoes

Explanation:

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Answer 2

For this case we have the following function:
m (x) = 26x-x2
Deriving we have:
m '(x) = 26-2x
We equal zero and clear the value of x:
26-2x = 0
2x = 26
x = 26/2
x = 13
Substituting x in the function we have:
m (13) = 26 * (13) - (13) ^ 2
m (13) = 169
Answer:
the amount of rainfall that will maximize the number of mosquitoes is:
x = 13 inches
The maximum number of mosquitoes is:
m (13) = 169