The amount of pollution content added in air in a city due to `x-d i e s e l` vehicles is given by `P(x)=0. 005 x^3+0. 02 x^2+30 x` Find the marginal increase in pollution content when `3` diesel vehicles are added and write which value is indicated in the above question.

Explanation

Given that,

`P(x)=0. 005 x^3+0. 02 x^2+30 x`

Marginal increase in pollution content `=(dP)/(dx)`

`(dP)/(dx)=3*0.005x^2+2*0.02x+30`

`(dP)/(dx)=0.015x^2+0.04x+30`


At `x=3`

`(dP)/(dx)=0.015(3)^2+0.04(3)+30`

`(dP)/(dx)=0.135+0.12+30`

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