The mosquito population is a function of rainfall, and can be approximated by the formula N(x)=−x3+45x2+1000 where x is the number of inches of rainfall. Find the values of x (if any) so that the population will be a maximum? Note that x is non-negative.

Therefore the population will be maximum when x=30 inches.

Step-by-step explanation:

Given that, the mosquito population is a function of rainfall and can be approximated by the formula

where x is the number of inches of rainfall.

Differentiating with respect to x

Again differentiating with respect to x

Now we set N'(x)=0

Since at x=30, N''(x)<0, So at x=30, N(x) has maximum value.

Therefore the population will be maximum when x=30 inches.

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step-by-step explanation: