Question

x tends 0 to $\pi$ then the given function

$f(x) = x\sin x + \cos x + \cos^{2}x$ is

• A. Increasing
• B. Decreasing
• C. Neither increasing nor decreasing
• D. None of these

Answer 1

Answer: (B)

Decreasing

Answer 2

$f(x) = x\sin x + \cos x + \cos^{2}x\therefore$ $f^{'}(x) = \sin x + x\cos x - \sin x - 2\cos x\sin x$ = $\cos x(x - 2\sin x)$

Hence $x \rightarrow 0$ to $\pi$, then $f^{'}(x) \leq 0$, i.e., $f(x)$ is decreasing function.