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Second Derivative of the Graph of a Function

This is part of the HSC Mathematics Advanced course under the topic of Calculus: Differential Calculus.

In this post, we will explore the second derivative of the graph of a function. This will include learning how to:

  • Define and interpret the concept of the second derivative as the rate of change of the first derivative function in a variety of contexts, for example, recognise acceleration as the second derivative of displacement with respect to time
  • Understand the concepts of concavity and points of inflexion and their relationship with the second derivative
  • Use the second derivative to determine concavity and the nature of stationary points
  • Understand that when the second derivative is equal to 0 this does not necessarily represent a point of inflexion

Concavity, Inflection Points, and Second Derivative

 

Eddie Woo: Using the Second Derivative (1 of 5: Finding the Point of Inflexion)

Using the Second Derivative (2 of 5: Turning Point vs Stationary Point analogy)

 

Using the Second Derivative (3 of 5: Why the Points of Inflexion may not exist when f”(x) = 0)

 

Using the Second Derivative (4 of 5: Examples where f”(x)=0 doesn’t mean Point of Inflexion)

 

Using the Second Derivative (5 of 5: Where the concavity changes but f”(x) doesn’t exist)

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