Find the interval in which the function f(x) = x^2 + 2x – 5 is st… - Vidyadip

Question

Find the interval in which the function $f(x) = x^2 + 2x – 5$ is strictly increasing or decreasing.

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Answer

The given function is, $f(x) = x^2 + 2x - 5$
Derivative, $f'(x) = 2x + 2$
If $f'(x) = 0,$
$\Rightarrow x = -1$
So, the point $x = -1$ divides the real line into two disjoint intervals $(-\infty,-1)$ and $(-1, \infty)$
So, in interval $(-\infty,-1)$
$f'(x) = 2x + 2 < 0$
Therefore, the given function $(f)$ is strictly decreasing in interval $(-\infty,-1)$
Now, in interval $(1, \infty)$, we have
$f'(x) = 2x + 2 > 0$
Therefore, the given function $(f)$ is strictly increasing in interval $(-1, \infty)$
Thus, $f$ is strictly increasing for $x > -1$

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