This site provides users with aninteractive applet for exploring the relationships between the characteristics of the graph (increasing, decreasing, concave up, concave down) and the characteristics of its derivatives.

The key features of this interactive applet are:

A 4th-degree polynomial is graphed.

It explores the relationship between the characteristics of the graph.

It asks the user several questions while exploring the relationships between the characteristics of the graph (increasing, decreasing, concave up, concave down) and the characteristics of its derivatives.

In a tabular form, it asks the user: if f (positive, negative...) then f' and f'' is?

Type of Material:

Simulation

Recommended Uses:

This interactive applet can be used in the classroom to explain relative extrema. It can also be used for Exam review, class projects, Lecture Notes, assignments, or Handouts for Calculus I.

Technical Requirements:

Any browser

Identify Major Learning Goals:

To provide students with an interactive applet to visualize the relationships between the characteristics of the graph (increasing, decreasing, concave up, concave down) and the characteristics of its derivatives. Students can follow all instructions to construct their graphs. In addition, students can practice their understanding of this material by clicking on the question marks in the table at the bottom of this site.

The major learning goals are:

Learn the concept of relative maximum, relative minimum and inflection in a function f(x).

Identify the characteristics of the derivative of a given function.

Target Student Population:

Students of Calculus I course.

High School, College Lower Division

Prerequisite Knowledge or Skills:

Completion of College Algebra and Pre-Calculus

Content Quality

Rating:

Strengths:

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?

Concerns:

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.

Potential Effectiveness as a Teaching Tool

Rating:

Strengths:

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.

Concerns:

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.

Ease of Use for Both Students and Faculty

Rating:

Strengths:

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.

Concerns:

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.

Other Issues and Comments:

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 points in the graph are not shown.

Creative Commons:

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