What are the benefits of seeing color-coded graphs?
In addition to aiding your visualization of the increasing/decreasing segments and concave up/concave down segments, the color coding serves the purpose of identifying turning points and points of inflection even when a curve appears flat in a certain region. You can be sure that if a curve is flat but has both red and blue meeting at a juncture, there is a turning point at the juncture. In our Rational Examples, see the case of the “hidden” turning point. This “hidden” turning point can be revealed on resizing in the vicinity of the juncture of the two colors, most conveniently by using Smart Zooming. The same can be said for “hidden” changes in concavity. If a curve appears flat in a certain region that includes the juncture of green and purple colors, despite the appearance of being flat, the shape of that curve is changing concavity at the juncture and it may be possible to confirm this visually by resizing the graph in the vicinity of the juncture.
