NCERT Class 12 · Ch 6 Miscellaneous Exercise · Q11
NCERT Class 12 Maths · Chapter 6 Applications Of Derivatives · Miscellaneous Exercise Question 11
Find absolute extrema of cos²x+sin x on [0,π].
💡 Concept Hints
- Identify the domain and the inner and outer functions, or the relevant one-sided limits.
- Apply the appropriate differentiation or limit rule, keep all chain factors, and check exceptional points.
✅ Step-by-Step Solution
Final Answer: Maximum 5/4 at π/6 and 5π/6; minimum 1 at 0,π/2,π.
- Write u=sin x∈[0,1], so f=1+u−u²=5/4−(u−1/2)².
- The maximum 5/4 occurs at u=1/2, i.e. x=π/6,5π/6.
- The minimum on 0≤u≤1 is 1 at u=0 or 1, giving x=0,π,π/2.
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