Point [i]P[/i] on this function, which is a combination of functions [i]f[/i] and [i]g[/i], is literally a [i]point[/i] on the function; it is not smooth there.[br][br]Observe what happens when GeoGebra tries to draw a tangent line at [i]P[/i]. Depending on which of the two pieces of the function GeoGebra tries to follow, it creates two very different tangent lines with very different slopes.[br][br]If you check the "Show secant lines" option, you can view secant lines between C and P and between C and D, respectively. Drag points C and D closer to P to observe what happens.