Not all continuous functions are differentiable. Pupils find three types of functions that are defined everywhere but not differentiable for all values of x. Along with providing examples of each type of function, students explain the functions' properties in their own words.

Concepts

functions, differentiable, differential calculus, mathematical properties, continuous function, limits

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Additional Tags

math

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Instructional Ideas

• Provide instruction on where functions may not be differentiable
• Use graphic representations when first introducing the definition as a limit

Classroom Considerations

• Pupils should understand the definition of the derivative

Pros

• The rubric gives a couple of examples
• Includes suggested points for scoring

Cons

• None