Peer Review

This site provides an interactive applet about derivatives and the shape of graph using a quadratic polynomial function example in the applet. This site offers a great help for students of Calculus I who want to practice graphing functions and the characteristics of graphs. This site can be included as a part of lecture or as an extra online tutorial for students. This site can serve a practice interactive example at the Calculus I lab session.

It's features are:

• A quartic polynomial is graphed and the relationships between the characteristics of the graph (increasing, decreasing, concave up, concave down)  and the characteristics of its derivatives can be explored.
• It asks users a number of questions related to relative extrema.
• In a tabular form, it asks the user: if f (positive, negative...) then f' and f'' is? 

• It does not explain the concept of critical points of the function, i.e. if f(x) has  a relative extremum at x=c, then the first derivative is either zero or undefined at c explicitly. Though it is shown in the table.
• Inflection point in the graph not shown.
• It will be a good idea to show the tangent line for better understanding.

Both instructor and student can use this site in the Calculus I class in lectures or assignments related to graphing functions and the characteristics of graphs.

• It is an effective interactive tool to teach Extrema and Critical Points of f(x).
• The number of questions asked on the website will help students and instructors to better appreciate the subject.

A lot of effort is needed by the instructor to explain the concept of relative extrema and critical points by explaining step by step if f(x) increases or decreases, is concave up or concave down, has an inflection point at x=c etc.

Students and instructors can access this applet easily, and they can choose one of the available options on the left-hand side of this applet. All they need is to follow all the given instructions because these instructions provide step-by-step guidelines to construct their graphs.

Interesting questions are asked on the website, but it will require the instructor to explain all the concepts in the classroom or the student needs to know the concept beforehand.