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The amount of pollution content added in air in a city due to x-diesel vehicles is given by P(x) = 0.005x^3 + 0.02x^2 + 30x. - Mathematics

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The amount of pollution content added in air in a city due to x-diesel vehicles is given by P(x) = 0.005x3 + 0.02x2 + 30x. Find the marginal increase in pollution content when 3 diesel vehicles are added and write which value is indicated in the above question.

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Solution

Given,P(x) = 0.005x3 + 0.02x2 + 30x.

Differentiating both sides with respect to x, we have 

marginal increase in pollution content = `(dP(x)/(dx))=0.015x^2+0.04x+30......(1)`

Putting x = 3 in (1), we have `((dP(x))/dx)_(x=3)=0.015xx9+0.04xx3+30=30.255`

Therefore, the value of marginal increase in pollution content is 30.255

Concept: Increasing and Decreasing Functions
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