Question

Find the interval in which the following function is increasing or decreasing
$f\left(x\right)=6-9x-x^2$

Answer 1

Given the function $f\left(x\right)=6-9x-x^2$ for $x\in R$.

Now $f^{\prime }\left(x\right)=-9-2x$.

Now $f^{\prime }\left(x\right)\ge 0$ if $x\le -\frac{9}{2}=-4.5$ and $f^{\prime }\left(x\right)\le 0$ if $x\ge -\frac{9}{2}=-4.5$.

So the function will be decreasing on $[-4.5,\infty )$ and that will be increasing on $(-\infty ,-4.5]$.