AQA A Level Maths: Pure复习笔记7.4.2 Points of Inflection

Points of Inflection

What is a point of inflection?

  • At AS level you encountered points of inflection when discussing stationary points
    • When the sign of the first derivative (ie of the gradient) is the same on both sides of a stationary point, then the stationary point is a point of inflection

    7.4.2-Pts-of-Infl-Illustr-1

  • A point of inflection does not have to be a stationary point however
  • A point of inflection is any point at which a curve changes from being convex to being concave
    • This means that a point of inflection is a point where the second derivative changes sign (from positive to negative or vice versa)

    7.4.2-Pts-of-Infl-Illustr-2

  • To find the points of inflection of a curve with equation y = f(x):

7.4.2-Pts-of-Infl-Illustr-3

7.4.2-Pts-of-Infl-Illustr-3_proviso

Exam Tip

  • Remember – the first derivative (ie the gradient) does NOT have to be zero at a point of inflection!

Worked Example

7.4.2-Pts-of-Infl-Example

 

 

 

 

 

转载自savemyexams

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