Q247 / 270 · NDA 2018 (Phase 1) · Mathematics

If $f(x)$ is an even function, where $f(x) \neq 0$, then which one of the following is correct?

  • A
    $\mathrm{f}^{\prime}(\mathrm{x})$ is an even function
  • Correct answer
    B
    $f^{\prime}(x)$ is an odd function
  • C
    $f^{\prime}(x)$ may be an even or odd function depending on the type of function
  • D
    $\mathrm{f}^{\prime}(\mathrm{x})$ is a constant function

Solution

$\mathrm{f}(\mathrm{x})$ is an even function. Let's see some examples (1) If $f(x)=\cos x$, which is even function, $f^{\prime}(\mathrm{x})=-\sin \mathrm{x}$, which is odd function. (2) If $f(x)=x^2$, which is even function, $f^{\prime}(\mathrm{x})=2 \mathrm{x}$, which is odd function.

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

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