Q45 / 120 · VITEEE 2017 · Mathematics

The function $f(x)=\sin x-k x-c$, where $k$ and $c$ are constants, decreases always when

  • A
    $k>1$
  • Correct answer
    B
    $k \geq 1$
  • C
    $k < 1$
  • D
    $k \leq 1$

Solution

Let $f(x)=\sin x-k x-c$ where $k$ and $c$ are constants $f^{\prime}(x)=\cos x-k$ $\therefore f$ decreases if $\cos x \leq k$ Thus, $f(x)=\sin x-k x-c$ decrease always when $k \geq 1$

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

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