Class 12 Applications Of Derivatives · Short Answer2 Marksmonotonicity
Class 12 Maths · Applications Of Derivatives · Short Answer #46
Determine whether f(x)=cos(2x+π/4) is increasing or decreasing on (3π/8,7π/8).
✅ Step-by-Step Solution
Final Answer: Strictly increasing.
- f′(x)=−2sin(2x+π/4).
- For 3π/8<x<7π/8, π<2x+π/4<2π, so sine is negative and f′>0.
- Therefore f is strictly increasing on the entire stated interval.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] f′(x)=−2sin(2x+π/4).
- [1 mark] For 3π/8<x<7π/8, π<2x+π/4<2π, so sine is negative and f′>0.
- [0.5 marks] Therefore f is strictly increasing on the entire stated interval.
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