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
 
 the amount of rainfall that will maximize the number of mosquitoes is:
 x = 13 inches
 The maximum number of mosquitoes is:
 m (13) = 169