Question

The function $f(x)=tanx-x$

• A. always increases
• B. always decreases
• C. never increases
• D. sometimes increases and sometimes decreases

Answer 1

Answer: (A)

$f(x)=tanx-x$
$\Rightarrow f(x)=se{c}^{2}x-1=ta{n}^{2}x$
$ta{n}^{2}x$ is always $+ve$, so $f^{\prime }(x)>0$
$\therefore f(x)$ always increases.