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)

$f(x) = tan\, x - x$
$\Rightarrow f(x) = sec^2x - 1 = tan^2x$
$tan^2x$ is always $+ve$, so $f'(x) > 0$
$\therefore f(x)$ always increases.