Find the intervals in which the following functions are increasin… - Vidyadip

Question

Find the intervals in which the following functions are increasing or decreasing. $f(x) = x^{2 }+ 2x - 5$

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Answer

We have,
$f(x) = x^{2 }+ 2x - 5$
$\therefore f'(x) = 2x + 2$
Now.
$f'(x) = 0 $
$\Rightarrow x = -1$
Point $x = -1$ divides the real line into two disjoints intervals i.e., $(-\infty,-1)$ and $(-1,\infty).$
In interval $(-\infty,-1), f'(x) = 2x + 2 < 0.$
$\therefore f $is strictly decreasing in interval $(-\infty,-1).$
Thus, $f$ is strictly decreasing for $x < -1.$
In interval $(-1,\infty), f'(x) = 2x + 2 > 0.$
$\therefore$ f is strictly increasing in interval $(-1,\infty).$
Thus, $f$ is strictly increasing for $x > -1.$

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