NCERT Class 12 · Ch 6 Exercise 6.2 · Q17
NCERT Class 12 Maths · Chapter 6 Applications Of Derivatives · Exercise 6.2 Question 17
Prove log|cos x| decreases on (0,π/2) and increases on (3π/2,2π).
💡 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: The stated intervals hold.
- For cos x≠0, the derivative of log|cos x| is −tan x.
- Tangent is positive on (0,π/2), giving a negative derivative, and negative on (3π/2,2π), giving a positive derivative.
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