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 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 questions.

Answer :

Given that P(x) = 0.0005x^{3} + 0.02x^{2} + 30x

The marginal increase in the pollution level is

On differentiating both sides, we get

P’(x)=0.0005×3x^{2} +0.02×2x +30

= 0.0015x^{2} + 0.04x +30

Substituting x=3, we get

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

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