Question

If $f\left(x\right)=\sin x-\cos x-ax+b$ decreases for a where $x\in R$ then?

• A. $a<1$
• B. $a>1$
• C. $a<\sqrt{2}$
• D. $a>\sqrt{2}$

Answer 1

Answer: (C), (D)

The correct options are
C $a>\sqrt{2}$
D $a<\sqrt{2}$

$f\left(x\right)=sinx-cosx-ax+b$

$f^1\left(x\right)=cosx+sinx-a<0$

$\Rightarrow cosx+sinx<a$

As, $cosx+sinx<\sqrt{2}$ (always)

So, $a<\sqrt{2}$ or $a>\sqrt{2}$