How do you find the absolute and local extreme values for #y=-x+7# on the interval [-10,10]?

1 Answer
Jan 15, 2017

Absolute maximum (point): #(-10, 17)#, and #y=17# maximum value
Absolute minimum (point): #(10, -3)#, and #y=-3# minimum value

Explanation:

#y = -x + 7# is a line, meaning it has no absolute or local extreme values. However, since we are restricting it to the interval #[-10, 10]#, and the slope is negative, we see that the points with #x# coordinates #-10# or #10#, are the absolute maximum and absolute minimum points, respecitvely. The absolute maximum in this interval is, therefore, #(-10, 17)# and the absolute minimum is #(10, -3)#.

Trying to use the first derivative doesn't help, since it's always #-1#, so it is never zero, and always defined.