The interval of increase of the function $f(x)=x-e^x+\tan (2 \pi / 7)$, is
(a) $(0, \infty)$
(b) $(-\infty, 0)$
(c) $(1, \infty)$
(d) $(-\infty,-1)$
Answer & explanation
Correct answer: option 4
We have,
$f(x)=x-e^x+\tan \left(\frac{2 \pi}{7}\right) \Rightarrow f^{\prime}(x)=1-e^x$
For f(x) to be increasing, we must have
$f^{\prime}(x)>0 \Rightarrow 1-e^x>0 \Rightarrow e^x<1 \Rightarrow x<0 \Rightarrow x \in(-\infty, 0)$