The mosquito population is a function of rainfall,

Ответ:

s108870

23.01.2022

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

N(x)= -x^3+45x^2+1000

where x is the number of inches of rainfall.

N(x)= -x^3+45x^2+1000

Differentiating with respect to x

N'(x)= -3x^2+90x

Again differentiating with respect to x

N''(x)=-6x+90

Now we set N'(x)=0

-3x^2+90x=0

$\Rightarrow -3x(x-30)=0$

$\Rightarrow x=0,30$

N''(0)=-6.0+90=900

N''(30)=-6.30+90=-90

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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