Q

# Find the intervals in which the following functions are strictly increasing or decreasing x ^ 2 + 2 x - 5

6. Find the intervals in which the following functions are strictly increasing or
decreasing:

a) $x ^2 + 2x -5$

Views

f(x)  = $x ^2 + 2x -5$
$f^{'}(x) = 2x + 2 = 2(x+1)$
Now,
$f^{'}(x) = 0 \\ 2(x+1) = 0\\ x = -1$

The range is from $(-\infty,-1) \ and \ (-1,\infty)$
In interval $(-\infty,-1)$   $f^{'}(x)= 2(x+1)$ is -ve
Hence, function f(x)  = $x ^2 + 2x -5$ is strictly decreasing in interval  $(-\infty,-1)$
In interval $(-1,\infty)$  $f^{'}(x)= 2(x+1)$ is +ve
Hence, function f(x)  = $x ^2 + 2x -5$ is strictly increasing in interval  $(-1,\infty)$

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