If `C=0.003x^3+0.02x^2+6x+250` gives the amount of carbon pollution in air in an area on the entry of x number of vehicles, then find the marginal carbon pollution in the air, when 3 vehicles have entered in the area and write which value does the question indicate.

Explanation

Carbon pollution in air, `C = 0.003x^3+0.02x^2+6x+250`

Marginal carbon pollution in air, `(dC)/dx = 0.003(3x^2)+0.02(2x)+6`

`=>0.009x^2+0.04x+6`

At `x=3`,

`(dC)/dx|_(x=3) = 0.009(9)+0.04(3)+6`

`(dC)/dx|_(x=3) = 0.081+0.12+6 = 6.201`

So, marginal carbon pollution is `6.201`.