NCERT Class 12 · Ch 6 Exercise 6.2 · Q3
NCERT Class 12 Maths · Chapter 6 Applications Of Derivatives · Exercise 6.2 Question 3
Show sin x is (a) increasing on (0,π/2), (b) decreasing on (π/2,π), and (c) neither 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: All three statements hold.
- The derivative is cos x, positive on (0,π/2) and negative on (π/2,π).
- Thus sin x rises to 1 at π/2 and then falls; it cannot be monotone throughout (0,π).
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