The Relationship Between Continuity & Differentiability


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question 1 of 3

Which of the following relationships are true?
A: All differentiable functions are continuous functions.
B: All continuous functions are differentiable functions.
C: Not all differentiable functions are continuous functions.
D: Not all continuous functions are differentiable functions.

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1. Which of the following is true for continuous functions?

2. What is a derivative?

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About This Quiz & Worksheet

In the field of mathematics, there are many theories and concepts related to graphing, and this quiz will evaluate your knowledge of the concepts of continuity and differentiability. Many of the questions measure your knowledge of these and related terms as well as your ability to apply these concepts to sample equations and word problems.

Quiz & Worksheet Goals

With the help of these assessment tools, you can quickly verify what you know about:

  • Identifying true relationships
  • Continuous function facts
  • Definition of a derivative
  • Non-differentiable graphs
  • Determining if functions are continuous and differentiable

Skills Practiced

This quiz and worksheet can assist you with polishing the following skills:

  • Problem solving - use acquired knowledge to solve continuous and differentiable graphing practice problems
  • Interpreting information - verify that you can read information regarding true relationships and interpret it correctly
  • Information recall - access the knowledge you've gained regarding non-differentiable graphs

Additional Learning

For supplemental information beyond the answers to the quiz, try reviewing the connected lesson, The Relationship Between Continuity & Differentiability. Some of the additional topics mentioned in this lesson include:

  • Comparison of continuous and discontinuous functions
  • Types of relationships and characteristics
  • Examples of functions as graphs