IB DP Maths: AI HL復習筆記5.2.6 Concavity & Points of Inflection
Concavity of a Function
What is concavity?
- Concavity?is the way in which a?curve?(or surface)?bends
- Mathematically,
CONCAVE?DOWN?is often called?concave- CONCAVE?UP?is often called?convex
Exam Tip
- In an exam an easy way to remember the difference is:
- Concave?down?is the shape of (the mouth of) a sad smiley?☹?
- Concave up?is the shape of (the mouth of) a happy smiley?☺?
Worked Example
Points of Inflection
What is a point of inflection?
What about the first derivative, like with turning points?
- If it does, it is also a?stationary?point?and is often called a?horizontal?point?of?inflection
- the tangent to the curve at this point would be horizontal
- The?normal distribution?is an example of a commonly used function that has a graph with two non-stationary points of inflection
- If it does, it is also a?stationary?point?and is often called a?horizontal?point?of?inflection
How do I find the coordinates of a point of inflection?
Exam Tip
Worked Example
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