Class 12 Applications Of Derivatives · Short Answer2 Marksabsolute_extrema
Class 12 Maths · Applications Of Derivatives · Short Answer #95
Prove that f(x)=sin x+√3cos x has a maximum at x=π/6, and find that value.
✅ Step-by-Step Solution
Final Answer: Maximum 2 at x=π/6 (also π/6+2kπ).
- Use the identity sin x+√3cos x=2sin(x+π/3).
- Since sin u≤1, f≤2, with equality when x+π/3=π/2+2kπ.
- The maximum 2 occurs at x=π/6+2kπ, including x=π/6.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Use the identity sin x+√3cos x=2sin(x+π/3).
- [1 mark] Since sin u≤1, f≤2, with equality when x+π/3=π/2+2kπ.
- [0.5 marks] The maximum 2 occurs at x=π/6+2kπ, including x=π/6.
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