Question

The interval in which the function $f\left(x\right)=x+e^{-x}+\tan \frac{\pi }{12}$ is increasing is

• A. $(-\infty ,0)$
• B. $(1,\infty )$
• C. $(-1,\infty )$
• D. $(0,\infty )$

Answer 1

Answer: (D)

$(0,\infty )$

$f\left(x\right)=x+e^{-x}+tan\frac{\pi }{12}$
differenciating w.r.t x
$\Rightarrow f^{{}^{\prime }}=1-e^{-x}$
$1-e^{-x}>0$
$\Rightarrow e^{-x}<1$
$\Rightarrow e^x>1$
$\Rightarrow x>0$
$\therefore$ the required interval is $(0,\infty ).$