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.

✓

Answer

The given function is, f(x) = x² + 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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