ASMathsEdexcelPureRevision NotesDifferentiationDifferentiationDefinition of Gradient

Definition of Gradient (Edexcel AS Maths) : Revision Note

Roger B

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Roger B

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Edexcel Maths: PureCambridge (CIE) Maths: Pure 1AQA Maths: PureOCR Maths A: Pure

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Definition of Gradient

What is the gradient of a curve?

  • At a given point the gradient of a curve is defined as the gradient of the tangent to the curve at that point

  • A tangent to a curve is a line that just touches the curve at one point but doesn't cut the curve at that point

Def Grad Illustr 1, A Level & AS Maths: Pure revision notes

  • A tangent may cut the curve somewhere else on the curve

Def Grad Illustr 2, A Level & AS Maths: Pure revision notes

  • It is only possible to draw one tangent to a curve at any given point

  • Note that unlike the gradient of a straight line, the gradient of a curve is constantly changing

Examiner Tips and Tricks

  • A tangent only exists at points where a curve is smooth.

  • For example, there is no tangent (or gradient) at one of the 'corners' in a modulus function. 

    Def Grad Illustr 3, A Level & AS Maths: Pure revision notes

Worked Example

Def Grad Example, A Level & AS Maths: Pure revision notes

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Roger B

Author: Roger B

Expertise: Maths Content Creator

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.

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