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ryzh [129]
3 years ago
9

The mosquito population is a function of rainfall, and can be approximated by the formula N(x)=−x3+45x2+1000 where x is the numb

er 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.
Mathematics
1 answer:
KiRa [710]3 years ago
5 0

Answer:

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=90>0

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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