AQA A Level Maths: Pure复习笔记7.2.1 Gradients, Tangents & Normals

Gradients, Tangents & Normals

Using the derivative to find the gradient of a curve

  • To find the gradient of a curve y= f(x) at any point on the curve, substitute the x‑coordinate of the point into the derivative f'(x)

7.2.1-Grad-Tang-Norm-Illustr-1

Using the derivative to find a tangent

  • At any point on a curve, the tangent is the line that goes through the point and has the same gradient as the curve at that point

7.2.1-Grad-Tang-Norm-Illustr-2

Using the derivative to find a normal

  • At any point on a curve, the normal is the line that goes through the point and is perpendicular to the tangent at that point

7.2.1-Grad-Tang-Norm-Illustr-3

Exam Tip

  • The formulae above are not in the Edexcel exam formulae booklet, but if you understand what tangents and normals are, then the formulae follow from the equation of a straight line combined with parallel and perpendicular gradients (see Worked Example below).

Worked Example

7.2.1-Grad-Tang-Norm-Example

 

 

 

 

转载自savemyexams

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