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.

Given: P(x) = 0.005x³ + 0.02x² + 30x

Firstly, we differentiate with respect to x, we get

∴ Marginal increase in pollution content = 0.015x² + 0.04x + 30

The marginal increase in pollution content when 3 diesel vehicles are added =

= 0.135 + 0.12 +30

= 30.255

∴ Value of marginal increase pollution content is 30.255

Increase in number of diesel vehicles increases the pollution.

Value: We should aim at saving the environment by reducing the pollution by decreasing the vehicle density on road.