Derivatives Exercises

Answer

1. This line is a secant line because it crosses the graph at two points. This line is not a tangent line because it crosses the graph at x = a rather than bouncing off.
2. This is a tangent line. The line bounces off the graph at x = a.
3. This is a tangent line. The line bounces off the graph at x = a without crossing it.
4. This is both a tangent line and a secant line. The line lies tangent to the graph at x = a, but then intersects the graph again in the first quadrant.
5. This is a tangent line. The line bounces off the graph at x = a. This is one of the rare occasions, though, where the line actually crosses the graph at the point of tangency.

Answer

Answer

Answer

Answer

1. Yes. This line definitely "lays along" f. Since f is a line, the tangent line to f at a is the line f again.
2. This is a tangent line, just not at x = a. The line is tangent to graph at a point a little way to left of a.
3. This is a tangent line. The line just touches the graph at x = a and then bounces right off of it.
4. This is not a tangent line. The line passes right through the graph at x = a very non-tangentially.
5. This is not a tangent line. The line doesn't bounce off the graph at any point.