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?

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