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  4. The value of ' a ' for which the function f(x)= sin x- cos x-a x+b decreases for all real values of x, is -

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Q. The value of ' $a$ ' for which the function $f(x)=\sin x-\cos x-a x+b$ decreases for all real values of $x$, is -

Application of Derivatives

Solution:

$f ( x )=\sin x -\cos x - ax + b$
$f ^{\prime}( x )=\cos x +\sin x - a \leq 0 \forall x \in R$
$\Rightarrow a \geq \cos x +\sin x \forall x \in R$
$\Rightarrow a \geq \sqrt{2}$