1. Tangents and Normals

by M. Bourne

 

We often need to find tangents and normals to curves when we are analysing forces acting on a moving body.

A tangent to a curve is a line that touches the curve at one point and has the same slope as the curve at that point.

A normal to a curve is a line perpendicular to a tangent to the curve.

tangent


Note 1: As we discussed before (in Slope of a Tangent to a Curve), we can find the slope of a tangent at any point (x, y) using dy/dx.

Note 2: To find the equation of a normal, recall the condition for perpendicularity:

m1 × m2 = -1

 

Examples:

1. Find the gradient of

(i) the tangent (ii) the normal

to the curve y = x3 - 2x2 + 5 at the point (2,5)


Answer

2. Find the equation of the normal in the above example.


Answer

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3. Sketch the curve and the normal in the above example.

Let's first see how it looks in LiveMath...

LIVEMath


Now for the normal answer:

Answer



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