Q. The value of $b$ for which the function $f(x) = \sin{x - bx + c}$ is decreasing in the interval $( - \infty,\ \infty)$ is given by
A) $b < 1$
B) $b \geq 1$
C) $b > 1$
D) $b \leq 1$
Explanation
(c)
Given that$\ f(x) = sin\ x - bx + c$
$\therefore f^{'}(x) = \cos{x - b}$
For decreasing, $f^{'}(x) < 0,for\ all\ x \in R$.
$\Rightarrow \cos{x < b\ for\ all\ x \in R \Rightarrow b > 1.}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.