Question

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

Answer 1

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.