Class 12 Continuity And Differentiability · Short Answer2 Marksdifferentiability
Class 12 Maths · Continuity And Differentiability · Short Answer #117
For f(x)=|cos x−sin x|, find f′(π/6).
✅ Step-by-Step Solution
Final Answer: −(1+√3)/2
- At π/6, cos x−sin x=(√3−1)/2>0, and by continuity this remains positive in a neighborhood.
- Therefore f(x)=cos x−sin x locally, so f′(x)=−sin x−cos x.
- At π/6 this equals −1/2−√3/2=−(1+√3)/2.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] At π/6, cos x−sin x=(√3−1)/2>0, and by continuity this remains positive in a neighborhood.
- [1 mark] Therefore f(x)=cos x−sin x locally, so f′(x)=−sin x−cos x.
- [0.5 marks] At π/6 this equals −1/2−√3/2=−(1+√3)/2.
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