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A LevelMaths: PureOCRRevision Notes7. Differentiation7.4 Further Applications of Differentiation7.4.2 Points of Inflection

Points of Inflection (OCR A Level Maths: Pure)

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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

    Pts of Infl Illustr 1, AS & A Level Maths revision notes

  • 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)

    Pts of Infl Illustr 2, A Level & AS Level Pure Maths Revision Notes

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

 Pts of Infl Illustr 3, AS & A Level Maths revision notes

Pts of Infl Illustr 3_proviso, AS & A Level Maths revision notes

Examiner Tip

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

Worked example

Pts of Infl Example, AS & A Level Maths revision notes

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    Roger

    Author: Roger

    Expertise: Maths

    Roger's teaching experience stretches all the way back to 1992, and in that time he has taught students at all levels between Year 7 and university undergraduate. Having conducted and published postgraduate research into the mathematical theory behind quantum computing, he is more than confident in dealing with mathematics at any level the exam boards might throw at you.