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Question
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.
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
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