Parallel FunctionsDisplacing a function by a constant amount (vertically) has no effect on the slopes. Here the solid blue function is displaced by "k" from the dotted blue one. Slide k to see that the tangents stay parallel. Slide "A" to see that this holds throughout the function. It turns out that the converse of this property is also true; that is, that if two functions share a common derivative, they must differ by a constant. See chapter 4 of the textbook for details, or just wait! Dave Matthews, Created with GeoGebra |