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5.1 Finding Tangents and Normals

Finding Tangents

  • Differentiation can help us find the equation of the tangent to a curve at a certain point.
  • To recall, to be able to draw a line, we would need either coordinates of two points, or coordinates of a point and the gradient. For the latter, say the line passes through point \left(x_{1},\ y_{1}\right) and has gradient m, then the line has equation


  • When you are asked to find the equation of a tangent to a curve, usually they would give you the coordinates of the point of interest.

In this case, you can use differentiation to find out the gradient of tangent line at that point, and together with the point of intersection, you can find out the line’s equation.

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