#### Question

The amount of pollution content added in air in a city due to *x*-diesel 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.

#### Solution

Given,P(*x*) = 0.005*x*^{3} + 0.02*x*^{2} + 30*x*.

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

Is there an error in this question or solution?

Solution 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. Concept: Increasing and Decreasing Functions.