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Sketching Gradient Functions (OCR AS Maths A): Revision Note

Exam code: H230

Roger B

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Roger B

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OCR Maths A: PureCambridge (CIE) Maths: Pure 1AQA Maths: PureEdexcel Maths: Pure

Sketching gradient functions

How do I sketch the gradient function from the original function?

  • Using your knowledge of gradients and derivatives you can use the graph of a function to sketch the corresponding gradient function

  • The behaviour of a function tells you about the behaviour of its gradient function

Sketch Grad Illustr 1, A Level & AS Maths: Pure revision notes
Sketch Grad Illustr 2, A Level & AS Maths: Pure revision notes

Examiner Tips and Tricks

  • If f(x) is a smooth curve then f'(x) will also be a smooth curve.

  • Take what you know about f'(x) (based on the table above) and then 'fill in the blanks' in between.

  • If all you have is the graph of f(x) you will not be able to specify the coordinates of the y-intercept or any stationary points of f'(x).

  • Be careful – points where f(x) cuts the x-axis don't tell you anything about the graph of f'(x)!

Worked Example

Sketch 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.