The Graph of a Derivative
The animation below shows the graph of (in black) and of its derivative, (in green). The coordinates of point B (red) are the x- and y-coordinates of the derivative, while the coordinates of point A (blue) are the coordinates of . A segment of the tangent line at each position of A is shown in yellow and its slope is labeled in pink. Press the Animation button to start or stop the animation (it moves slowly, so give it a couple of seconds to start). Reset to the beginning () usng the Reset button.
Pay attention to the coordinate values of each point, as well as to the value of the slope of the tangent line as the animation proceeds. At some point you should be able to fill in the blank to the statement, "The slope of the tangent line is the same as __________________." (Note that the blank represents a phrase, not a single word.)