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BITSAT 2009
Exam
BITSAT
Year
2009
Subject
Mathematics
Chapter
Application of Derivatives

BITSAT 2009 · Mathematics · Application of Derivatives

The value of a in order that (f(x)= x- x-a x+b) decreases for all...

The value of aa in order that (f(x)=\sin x-\cos x-a x+b) decreases for all real values is given by

Options

  1. A(a \geq 2\sqrt{2})
  2. Ba (< 2\sqrt{2})
  3. C(a \geq 1)
  4. Da<1a < 1

Correct answer

A. (a \geq 2\sqrt{2})

Step-by-step solution

We have; (f(x)=\sin x-\cos x-a x+b) (\Rightarrow f^{\prime}(x)=\cos x+\sin x-a) (\Rightarrow \mathrm{f}^{\prime}(\mathrm{x}) <0 \forall \mathrm{x} \in \mathrm{R}) (\Rightarrow(\cos x+\sin x) < a \forall x \in \mathbb{R}) As the max. value of ((\cos x+\sin x)) is \2\sqrt{2} The above is possible when (a \geq \sqrt{2})$
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