CBSE Class 12 Math 2013 Solved Paper

Question : 10

Total: 29

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

Solution:

P(x) = 0.005 x3 + 0.02 x2 + 30x
Differentiating w.r.t. x,
Marginal increase in pollution content =

dP(x)

= 0.015 x2 + 0.04 x + 30
Putting x = 3 in (1), (

dP(x)

)x=3 = 0.015 × 9 + 0.04 × 3 + 30 = 30.255
Therefore, the value of marginal increase pollution content is 30.255.
Increase in number of diesel vehicles increases the pollution. We should aim at saving the environment by reducing the pollution by decreasing the vehicle density on road.

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