How can sketch a graph of a derivative?

Answer 1

To sketch a graph of a derivative, first look at the points where your original function f(x) has any horizontal tangents. If is does at that horizontal tangent plot a point correspondingly on the x-axis. From here analyze your functions in intervals. Where the f(x) function is increasing, your derivative function f prime of x should always be above the x axis, and conversely, where f(x) is decreasing your derivative function should always be below the axis As a crucial step, you should look at locations within the original function that are endpoints, cusps. and undefined points. This is essential as the derivative of the function will be undefined at those locations, and must be shown clearly on the graph (which is usually resolved with an open circle). To best understand sketching derivatives, try experimenting with a derivative plotter (java applet that can usually be found on-line for free. Also try to imagine the tangents to the original graph, as the graph progresses. Lastly, it should be noted that the magnitude of your derivative will depend on the rate of change of the function. However, most calculus teachers will let this be arbitrary.