Chapter 4: Applications of Derivatives - Section 4.4 - Concavity and Curve Sketching - Exercises 4.4 - Page 212: 10

$y''<0$, the curve is concave down for all x.

When $y$=$6-2x-x^2$ , then $y'$=$-2-2x $=$-2(1+x)$ and $y''$=$-2$. The curve rises on $(-\infty,1)$ and falls on $(-1,\infty)$. At $x$=$1$ there is a maximum. Since $y''< 0$, the curve is concave down for all $x$.