Part 3/5:
When graphing derivatives, we can focus on identifying the slope at various points of the original function. If we take a curve defined by ( y = f(x) ), the derivative ( f'(x) ) can be represented graphically by finding the zero points of the original function’s slope.
For instance, consider a curve that reaches a maximum (point ( A )) and minimum (point ( B )) at specific intervals. The derivatives at these points would be zero because the slope is flat at both extremes.
To visualize this, if the original graph goes upward, the derivative will have a positive slope, while if the graph descends, the derivative will be negative. By plotting these points, we create a new graph that represents the derivative of the original curve.