Sketching Gradient Functions (CIE A Level Maths: Pure 1)

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Sketching Gradient Functions

How can I sketch a function's gradient 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 Tip

  • 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

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.