Verified answer

Think about it.

f(x) = 6-2x is the graph of a straight line. That's why the derivative is just a horizontal line at -2. The derivative (slope) is always -2.

So, naturally, the extremas would be at the endpoints of the line at x=-1 and x=2. They plugged these numbers in and got the answer.

In order to find absolute extrema the x-values you take into consideration are the end points and where the derivative equals zero

Since the derivative is f'(x)=-2 and -2 does not and cannot equal zero the only values you have to use are the end points -1 and 2

if you plug 2 into f(x) you get 2

if you plug -1 into f(x) you get 8

8>2 so therefore 2 is your absolute min x-value and -1 is your absolute max x-value

hence (2, 2) and (-1, 8)