Question

The interval of increase of the function $y=x-e^x+\tan \left(\pi /7\right)$ is

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

Answer 1

Answer: (A), (C)

The correct options are
A $(-\infty ,-1)$
C $(-\infty ,0)$

$f\left(x\right)=x-e^x+tan\left(\pi /7\right)$
$f^{\prime }\left(x\right)=1-e^x$
For $f\left(x\right)$ to be increasing
$f^{\prime }\left(x\right)>0\Rightarrow 1-e^x>0$
$e^x<1$
$\Rightarrow xϵ(-\infty ,0)$
Hence option A,C are correct