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Tangents and Secants

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Introduction to Differentiation (2 of 9)

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Content

Content

This lesson aims to conceptually introduce tangents and secant, while also explaining the concept of an average gradient. By mastering the content in this session, you will:

  • Understand that tangents are the best linear approximations to a function at a point

  • Be able to find the equation of a general secant

  • Be able to approximate the equation of a tangent


  • Be able to find the average gradient between two points

  • Understand why the average gradient between two points doesn’t depend on the curve between the points


Syllabus Mapping

C1.1: Gradients of tangents

  • Describe the gradient of a secant drawn through two nearby points on the graph of a continuous function as an approximation of the gradient of the tangent to the graph at those points, which improves in accuracy as the distance between the two points decreases

C1.2: Difference quotients

  • Describe the behavior of a function and its tangent at a point, using language including increasing, decreasing, constant, stationary, increasing at an increasing rate

  • Interpret the meaning of the gradient of a function in a variety of contexts, for example on distance–time or velocity–time graphs

Student Progress

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