Q. 95.0( 2 Votes )

The amount of pollution content added in air in a city due to x diesel vehicles is given by P(x) = 0.0005 x3 + 0.02 x2 + 30 x. Find the marginal increase in pollution content when 3 diesel vehicles are added and write which value is indicated in the above questions.

Answer :

Given that P(x) = 0.0005x3 + 0.02x2 + 30x

The marginal increase in the pollution level is


On differentiating both sides, we get


P’(x)=0.0005×3x2 +0.02×2x +30


= 0.0015x2 + 0.04x +30


Substituting x=3, we get


P’(3) = 0.0015×9 + 0.04×3 +30 = 30.255 units


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