Q96 / 160 · AP EAMCET 2020 (18 Sep Shift 1) · Mathematics

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

  • A
    \(k < 0\)
  • Correct answer
    B
    \(k>0\)
  • C
    \(k=0\)
  • D
    Data Insufficient

Solution

Given function \(f(x)=k(x+\sin x)+k\) So, \(\quad f^{\prime}(x)=k(1+\cos x)\) \(\because f(x)\) is an increasing function, so \(\begin{aligned} & f^{\prime}(x) \geq 0 \\ & \Rightarrow \quad k(1+\cos x) \geq 0 \\ & \Rightarrow \quad k > 0 \quad\{\because 1+\cos x \geq 0\} \\ \end{aligned}\)

Hence, the correct answer is option: 'B'.

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