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?
Accepted Solution
A:
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