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Class 12 Applications Of Derivatives · Short Answer2 Marksmarginal_change

Class 12 Maths · Applications Of Derivatives · Short Answer #44

Pollution is modeled by P(x)=0.005x³+0.02x²+30x for x diesel vehicles. Find the marginal pollution increase at x=3.

✅ Step-by-Step Solution

Final Answer: 30.255 pollution units per vehicle
  1. Marginal increase is P′(x).
  2. Differentiate: P′(x)=0.015x²+0.04x+30. At x=3 this is 0.135+0.12+30.
  3. The marginal increase is 30.255 pollution units per vehicle.

📋 CBSE Stepwise Marking Scheme

  • [0.5 marks] Marginal increase is P′(x).
  • [1 mark] Differentiate: P′(x)=0.015x²+0.04x+30. At x=3 this is 0.135+0.12+30.
  • [0.5 marks] The marginal increase is 30.255 pollution units per vehicle.

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