Question

Find the intervals in which $x^2+2x-5$ is strictly increasing or strictly decreasing.

Answer 1

$f\left(x\right)=x^2+2x-5$

$f^{\prime }\left(x\right)=2x+2=2(x+1)$

Put $f^{\prime }\left(x\right)=0$

$\Rightarrow x+1=0$

$\Rightarrow x=-1$

Point $x=-1$ divide the real line in to $2$ disjoint intervals.

$(-\infty ,-1)$ and $(-1,\infty )$

$\therefore$ when the value of $x<-1$ then $x\in (-\infty ,-1)$ and $f$ is strictly decreasing.

And when the value of $x>-1$ then $x\in (-1,\infty )$ and $f$ is strictly increasing.

$\therefore f$ is strictly decreasing in $(-\infty ,-1)$ and is strictly increasing in $(-1,\infty )$