Question

Find the intervals in which the following functions are increasing or decreasing
$f\left(x\right)=x^2+2x-5$

Answer 1

Given the function $f\left(x\right)=x^2+2x-5$ for $x\in R$.

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

Now $f^{\prime }\left(x\right)\ge 0$ if $x\ge -1$ and $f^{\prime }\left(x\right)\le 0$ if $x\le -1$.

So the function will be increasing on $[-1,\infty )$ and that will be decreasing on $(-\infty ,-1]$.