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 questions.

Answer 1

Since, marginal increase in the pollution content is the rate of change of total pollution with respect to the number of diesel vehicles, we have

Marginal increase in pollution = $\frac{dP}{dx}=0.015x^2+0.04x+30$

When x = 3, marginal increase in pollution = $0.015\left(9\right)+0.04\left(3\right)+30=0.135+0.12+30=30.255$

Hence, the required marginal increase in pollution is 30.255 units.

It indicates the pollution level due to x diesel vehicles.