Class 12 Applications Of Derivatives · Short Answer2 Marksmonotonicity
Class 12 Maths · Applications Of Derivatives · Short Answer #41
Find the maximal intervals on which y=[x(x−2)]² is strictly increasing.
✅ Step-by-Step Solution
Final Answer: [0,1] and [2,∞)
- y′=4x(x−1)(x−2), with zeros 0,1,2.
- The derivative is positive on (0,1) and (2,∞), negative on the remaining open intervals. Strict increase extends to finite endpoints.
- Thus the maximal intervals are [0,1] and [2,∞).
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] y′=4x(x−1)(x−2), with zeros 0,1,2.
- [1 mark] The derivative is positive on (0,1) and (2,∞), negative on the remaining open intervals. Strict increase extends to finite endpoints.
- [0.5 marks] Thus the maximal intervals are [0,1] and [2,∞).
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