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APPLICATION OF DERIVATIVES — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsAPPLICATION OF DERIVATIVES1 Mark
MCQ
The function $\text{f(x)}=\tan\text{x}-\text{x}$
  • ✓
    Always increases.
  • B
    Always decreases.
  • C
    Never increases.
  • D
    Sometimes increases and sometimes decreases.
✓

Answer

Correct option: A.
Always increases.
We have, $\text{f(x)}=\tan\text{x}-\text{x}$
$\therefore\ \text{f}\ '(\text{x})=\sec^2\text{x}-1$
Since, $\text{f}\ '(\text{x}) > 0,\forall\text{ x}\in\text{R}$
Hence, $f(x)$ always increases.

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