Second Order Derivatives (DP IB Maths: AI HL)

• 
•      (First order derivative) 
•      (Second order derivative)

• differentiating twice (so) with respect to  twice (so)

• Similarly, the first order derivative can be just the first derivative

• a second order derivative is the rate of change of the rate of change of a function
  • i.e. the rate of change of the function’s gradient

Second order derivatives can be used to

• • • test for local minimum and maximum points
    • help determine the nature of stationary points
    • determine the concavity of a function
    • graph derivatives

• rewriting fractions, roots, etc as negative and/or fractional powers
• differentiating trigonometric functions, exponentials and logarithms
• using chain rule
• using product or quotient rule