Well, a curved line will have more than one slope. It's not a constant like it was on the straight lines. A straight line has the same slope everywhere on the line, but a curve won't. We are going to define slope at a point on a curved line as the slope of the tangent line drawn to the curve at that point. A equals the slope of the tangent line at A. Notice that the slope of a curved line can be positive, where the function is increasing, negative, where the function is decreasing, or 0, where it reaches that highest point.
Some curves can also have vertical tangent lines.
To the right is the graph of the height of a clock's minute hand as it travels around the clock. Answer these questions about the slope of the graph. Assignment Find some other phenomenon like stress to performance or speed over time and draw a graph of the function. Write at least 5 questions about the function. Make sure that some of the questions pertain to how slope and rate of change are related.