Revision:Tangents and Normals

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Tangents

If you differentiate the equation of a curve, you will get a formula for the gradient of the curve. Before you learnt calculus, you would have found the gradient of a curve by drawing a tangent to the curve and measuring the gradient of this. This is because the gradient of a curve at a point is equal to the gradient of the tangent at that point.

Example

Find the equation of the tangent to the curve at the point (2, 8).

Gradient of tangent when is .

From the coordinate geometry section, the equation of the tangent is therefore:

so

Normals

You may also be asked to find the gradient of the normal to the curve. The normal to the curve is the line perpendicular (at right angles) to the tangent to the curve at that point.

Remember, if two lines are perpendicular, the product of their gradients is -1.

So if the gradient of the tangent at the point (2, 8) of the curve is 8, the gradient of the normal is -1/8, since -1/8 × 8 = -1 .

Comments

Diagrams would help this article to explain exactly what we mean. Also a completion of the normal example to find the full equation would help.