AQA A Level Maths: Pure复习笔记7.1.1 Definition of Gradient

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


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


  • 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

Exam Tip

  • 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. 7.1.1-Def-Grad-Illustr-3

Worked Example