Question

The value of $b$ for which the function $f\left(x\right)=\sin x-bx+c$ is a strictly decreasing function $\forall x\in R$

• A. $b\in (-1,1)$
• B. $b\in (-\infty ,1)$
• C. $b\in (1,\infty )$
• D. $b\in [1,\infty )$

Answer 1

Answer: (C)

$b\in (1,\infty )$

A function is strictly decreasing in the range when $\frac{d\left(f\right(x\left)\right)}{dx}<0$

$\frac{d\left(f\right(x\left)\right)}{dx}=\frac{d(\sin x-bx+c)}{dx}=\cos x-b$

$\Rightarrow \cos x-b<0$ or $b>\cos x$

Since the range of $\cos x$ is $[-1,1]$ implies $b\in (1,\infty )$