At the top for one instant, its slope may be zero. When a ski goes through a depression or a valley bottom, the slope of this ski is first negative on the downhill side and then positive on the uphill side. A skier can recognize the intervals where the slope is increasing, and the intervals where the slope is decreasing. A slope which is becoming less negative or more positive as the skier moves forward in the positive x directions is said to be increasing. A slope which is becoming less positive or more negative as the skier moves forward in the positive x directions is said to be decreasing.
Snow is assumed.
At these jumps the slope or derivative is not defined. At vertical drops for instance, the slope is undefined. The slope of the ski is further undefined or not determined by the trail at kinks or sharp peaks where a short ski could pivot on its midpoint without touching the trail on either side. For instance, the top of an upside down V gives a sharp peak. Earthquakes, or vertical motions up and down of 2D hills and curves, suggest or imply that slope functions are not affected by the upward and downward shifts of part of a curve.