Answer
Increasing: $(-\infty,-1)$
Decreasing: $(-1,\infty)$
Work Step by Step
Everything left of $x=-1$ seems to be increasing and everything to its right is decreasing.
We can calculate it by finding the derivative:
$f(x)=-(x+1)^2$
$f(x)=-(x^2+2x+1)$
$f(x)=-x^2-2x-1$
$f'(x)=-2x-2$
$0=-2x-2$ [Set f'(x) = 0 to find critical values]
$x=-1$
Test values greater than -1 and less than -1:
$f'(0)=-2(0)-2$
$f'(0)=-2<0$
Therefore all numbers greater than -1 are decreasing.
$f'(-2)=-2(-2)-2$
$f'(-2)=2>0$
Therefore all numbers less than -1 are increasing.
