Class 12 Applications Of Derivatives · Short Answer2 Marksmonotonicity
Class 12 Maths · Applications Of Derivatives · Short Answer #38
Find the maximal intervals on which f(x)=2+3x−x³ is strictly decreasing.
✅ Step-by-Step Solution
Final Answer: (−∞,−1] and [1,∞)
- f′(x)=3−3x²=3(1−x)(1+x).
- The derivative is negative for x<−1 or x>1, and zero at −1,1. Strict decrease extends to those finite endpoints.
- The maximal intervals are (−∞,−1] and [1,∞); the assertion applies separately to each interval.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] f′(x)=3−3x²=3(1−x)(1+x).
- [1 mark] The derivative is negative for x<−1 or x>1, and zero at −1,1. Strict decrease extends to those finite endpoints.
- [0.5 marks] The maximal intervals are (−∞,−1] and [1,∞); the assertion applies separately to each interval.
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