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Application of Derivatives — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsApplication of Derivatives1 Mark
MCQ
The function $f(x)=\tan x-x$
  • ✓
    always increases
  • B
    always decreases
  • C
    never increases
  • D
    sometimes increases and sometimes decreases.
✓

Answer

Correct option: A.
always increases
(a) : $f(x)=\tan x-x$
$
\Rightarrow f^{\prime}(x)=\sec ^2 x-1=\tan ^2 x
$
$\tan ^2 x$ is always +ve, so $f^{\prime}(x)>0 \therefore f(x)$ always increases.

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