Class 12 Applications Of Derivatives · Short Answer2 Marksmonotonicity
Class 12 Maths · Applications Of Derivatives · Short Answer #42
Prove that y=4sinθ/(2+cosθ)−θ is strictly increasing on [0,π/2].
✅ Step-by-Step Solution
Final Answer: Strictly increasing on [0,π/2].
- By the quotient rule y′=4(2cosθ+1)/(2+cosθ)²−1.
- Simplify to y′=cosθ(4−cosθ)/(2+cosθ)², positive for 0≤θ<π/2.
- The function is continuous on the closed interval and has positive derivative in its interior, hence is strictly increasing on [0,π/2].
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] By the quotient rule y′=4(2cosθ+1)/(2+cosθ)²−1.
- [1 mark] Simplify to y′=cosθ(4−cosθ)/(2+cosθ)², positive for 0≤θ<π/2.
- [0.5 marks] The function is continuous on the closed interval and has positive derivative in its interior, hence is strictly increasing on [0,π/2].
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