Tangents and Normals

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Tangents

Given a curvewe can find the equation of the tangent toat a point whereby

  1. Finding

  2. Differentiating f(x) and substituting x=p to find

  3. Usingto find the equation of the tangent.

Example: Find the equation of the tangent to the curve

Multiply the brackets out to getand differentiate to get

and now find

Normals

Give a curvewe can find the equation of the normal toat a point whereby

  1. Finding

  2. Differentiating f(x) and substituting x=p to find

  3. Usingto find the equation of the normal.

Example: Find the equation of the normal to the curve

Multiply the brackets out to getand differentiate to get

and now find

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