Question

If x ≥ -6, and -2 ≤ y ≤ 6, what is the smallest possible value of xy?

Answer 1

smallest integar from the given conditions will be -36 (x=-6;y=6)
smallest possible value considering only whole numbers should be 0( x=0 or y=0)

Answer 2

Given $x\geq -6,-2\leq y\leq 6$. Since the minimum values of $x,y$ are negative and the maximum value are positive, the minimum value of

$xy$ is

$\min(xy)=\min(x)\max(y)\;or\;\min(y)\max(x)$

Now $\min(x)\max(y)=-6*6=-36\\ \min(y)\max(x)=-2*\infty=-\infty$

Therefore the minimum value of $xy$ is $-\infty$.