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

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$a \geq \sqrt{2}$

$a < 1$

$a < \sqrt{2}$

$a \geq 1$

answer is A.

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Detailed Solution

$\begin{array}{l} f (x) = \sin x - \cos x - a x + b \\ f^{'} (x) = \cos x + \sin x - a \\ f^{'} (x) < 0 \\ \cos x + \sin x < a \\ The maximum value of c o s x + \sin x = \sqrt{2} \\ Hence a \geq \sqrt{2} \end{array}$

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