Peer Review

This site is very visual and user friendly.  Users can enter any function f(x) to see the graph of the function as well as the graph of the derivative.  Through the use of a slider, users can move a point on the graph to call attention to what is happening at a particular x-value.  The slider range and step value can be adjusted to suit user preferences.

The graph clearly shows the connection between a function’s slope and its derivative, making it easier to understand how the first derivative test helps determine where a function is increasing or decreasing. Seeing how the graph changes in response to user input provides immediate feedback. This helps reinforce the idea that the sign of the derivative (positive or negative) dictates whether a function is rising or falling over an interval.

One major concern is that the Desmos graph provides a visual representation of the derivative but does not display the actual derivative function algebraically. This omission limits students' ability to connect the visual graph with the symbolic representation of the derivative.

The First Derivative Test interactive Desmos graph effectively enhances student learning by providing real-time feedback and visualization of the relationship between functions and their derivatives. Its user-friendly interface promotes active engagement and exploration, catering to diverse learning styles and encouraging collaboration. Additionally, the accessibility of the tool supports convenient out-of-class practice, fostering a deeper understanding of calculus concepts. 

This is a great visualization tool and would be beneficial to students learning to apply the first derivative test. 

This site could be improved by including a link to review material or a clear statement explaining the First Derivative Test.

Labeling and use of color make this graph visually appealing and easy to interpret.

Users can manipulate graphs in real-time, adjusting parameters to see immediate effects on the function and its derivative. This interactivity fosters a deeper understanding of the relationship between the two.