Tangents and Normals

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. Usingtofind 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

4. Finding

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

6. Usingtofind 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