Question

The value of ' $k$ ' for which the function $f(x)=k(x+\sin x)+k$ is increasing, is equal to

• A. $k<0$
• B. $k>0$
• C. $k=0$
• D. Data Insufficient

Answer 1

Answer: (B)

Given function $f(x)=k(x+\sin x)+k$
So, $f^{\prime }(x)=k(1+\cos x)$
$\because f(x)$ is an increasing function, so
$f^{\prime }(x)\ge 0$
$\Rightarrow k(1+\cos x)\ge 0$
$\Rightarrow k>0\{\because 1+\cos x\ge 0\}$