The interval of increase of the function f(x)=x-e^ x + (2 7 ) is: - Vidyadip

MCQ

The interval of increase of the function $\text{f}(\text{x})=\text{x}-\text{e}^{\text{x}}+\tan\Big(\frac{2\pi}{7}\Big)$ is:

A
$(0,\infty)$
✓
$(-\infty,0)$
C
$(1,\infty)$
D
$(-\infty,1)$

✓

Answer

Correct option: B.

$(-\infty,0)$

$\text{f}(\text{x})=\text{x}-\text{e}^{\text{x}}+\tan\Big(\frac{2\pi}{7}\Big)$
$f^{\prime}(x)=1-e^x$
For $f(x)$ to be increasing, we must have
$f ^{\prime}(x)>0$
$\Rightarrow 1- e ^{ x }>0$
$\Rightarrow e ^{ x }<1$
$\Rightarrow x <0$
$\Rightarrow\text{x}\in(-\infty,0)$
So$, f(x)$ is increasing on $(-\infty,0).$

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