Q. The interval of increase of the function $F(x) = x - e^{x} + \tan\left( \frac{2\pi}{7} \right)$ is
A) $(0,\ \infty)$
B) $( - \infty,\ 0)$
C) $(1,\ \infty)$
D) $( - \infty,\ - 1)$
Explanation
(b)
We have, $f(x) = x - e^{x} + \tan\left( \frac{2\pi}{7} \right)$
$\Rightarrow \ \ \ \ \ \ f^{'}(x) = 1 - e^{x}$
For $f(x)$ to be increasing, we must have
$f^{'}(x) > 0\ \ \Rightarrow \ \ \ 1 - e^{x} > 0$
$\Rightarrow \ \ \ e^{x} < 1$
$\Rightarrow \ \ \ x < 0\ \ \Rightarrow \ \ \ x \in ( - \infty,\ 0)$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.