Question

What is the value of b for which $f(x)=\sin x-bx+c$ is decreasing in the interval $(-\infty ,\infty )$ ?

• A. $b<1$
• B. $b\ge 1$
• C. $b>1$
• D. $b\le 1$

Answer 1

Answer: (C)

Given, $f(x)=\sin x-bx+c$ $\Rightarrow$ $f(x)=\cos x-b$ Since, it is decreasing, $\therefore$ $f(x)<0$ $\Rightarrow$ $\cos x<b$ $\Rightarrow$ $b>1$ $(\because \cos x\le 1)$