The long name is “Here’s the graph of the derivative, tell me things about the function.” Students are given either the equation of the derivative of a function or a graph identified as the derivative of a function but no equation is given. It is not expected that students will write the equation (although this…
Graphing and the analysis of graphs given (1) the equation, (2) a graph, or (3) a table of values of a function and its derivative(s) makes up the largest group of questions on the AP exams. Most of the other applications of the derivative depend on understanding the relationship between a function and its derivatives.…
Graphing and the analysis of graphs given (1) the equation, (2) a graph, or (3) a table of values of a function and its derivative(s) makes up the largest group of questions on the AP exams. Most of the other applications of the derivative depend on understanding the relationship between a function and its derivatives.…
The long name is “Here’s the graph of the derivative, tell me things about the function.” Most often students are given the graph identified as the derivative of a function. There is no equation given and it is not expected that students will write the equation (although this may be possible); rather, students are expected…
Recently there was a discussion on the AP Calculus Community bulletin board regarding whether it was necessary or desirable to have students do curve sketching starting with the equation and ending with a graph with all the appropriate features – increasing/decreasing, concavity, extreme values etc., etc. – included. As this is kind of question has…
The fourth in the Graphing Calculator / Technology series Comparing the graph of a function and its derivative is instructive and necessary in beginning calculus. Today I will show you how you can do this first with Desmos a free online graphing program and then on a graphing calculator. Desmos does this a lot better…
In a my last post I showed how to use a Desmos graph to discover, by looking at the tangent line as it moved along the graph of the function, the properties of the derivative of a function. This post goes in the opposite direction. Now, instead of discovering the properties of the derivative from the…
