IB DP Maths: AI HL复习笔记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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