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Class 12 Applications Of Derivatives · Conceptual Answer1 Marksmonotonicity_parameters

Class 12 Maths · Applications Of Derivatives · Conceptual Answer #36

Find all real a for which f(x)=sin x−ax+b is strictly increasing on R, where b is constant.

✅ Step-by-Step Solution

Final Answer: a≤−1
  1. f′=cos x−a≥0 for all x exactly when a≤−1. At a=−1 its zeros are isolated, so every nontrivial interval still has a positive increase; for a>−1 the derivative is negative near π.
  2. a≤−1

📋 CBSE Stepwise Marking Scheme

  • [0.5 marks] f′=cos x−a≥0 for all x exactly when a≤−1. At a=−1 its zeros are isolated, so every nontrivial interval still has a positive increase; for a>−1 the derivative is negative near π.
  • [0.5 marks] a≤−1

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