Class 12 Applications Of Derivatives · Short Answer2 Marksmonotonicity
Class 12 Maths · Applications Of Derivatives · Short Answer #94
Prove f(x)=tan x−4x is strictly decreasing on (−π/3,π/3).
✅ Step-by-Step Solution
Final Answer: Strictly decreasing.
- f′=sec²x−4.
- For |x|<π/3, cos x>1/2, so sec²x<4 and f′<0.
- Thus f is strictly decreasing on (−π/3,π/3).
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] f′=sec²x−4.
- [1 mark] For |x|<π/3, cos x>1/2, so sec²x<4 and f′<0.
- [0.5 marks] Thus f is strictly decreasing on (−π/3,π/3).
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