You can learn to graph as well as a calculator using calculus. The lesson introduces using derivatives to find critical points needed to graph polynomials. Pupils learn to find local maximums and minimums and intervals of increase and decrease using the first derivative. They find points of inflection by taking the second derivative, then use prior knowledge to draw a graph of the polynomial function.

Concepts

derivatives, graphing polynomial functions, maximums, minimums, intervals, concavity

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Additional Tags

math

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Instructional Ideas

• Provide functions for pairs to graph using derivatives
• Use graphing technology to check the graphs

Classroom Considerations

• You will need to create a separate sheet of the worksheet without the answers
• The lesson assumes class members understand what the second derivative is

Pros

• The examples are worked out, completely showing all the steps
• The lesson plan contains visual aids to help class members determine the direction of the graphs

Cons

• None