IB DP Maths: AA SL復習筆記5.2.3 Second Order Derivatives
Second Order Derivatives
What is the second order derivative of a function?
- If you?differentiate?the?derivative?of a?function?(i.e. differentiate the function a second time) you get the?second order derivative?of the function
The?second?order?derivative?can be referred to simply as the?second derivative
- Similarly, the?first order derivative?can be just the?first derivative
- A?first?order?derivative?is the?rate?of?change?of a function
- 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
- a?second?order?derivative?is the?rate?of?change?of the?rate?of?change?of a function
- Second?order?derivatives?can be used to
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- test for local minimum and maximum points
- help determine the nature of stationary points
- help determine the concavity of a function
- graph derivatives
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How do I find a second order derivative of a function?
- By?differentiating twice!
- This may involve
- rewriting?fractions, roots,?etc as?negative?and/or?fractional powers
- differentiating?trigonometric?functions,?exponentials?and?logarithms
- using?chain rule
- using?product?or?quotient?rule
Exam Tip
- Negative and/or fractional powers can cause problems when finding second derivatives so work carefully through each term
Worked Example
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