Finding Tangents and Normals

Tangents & Normals

MathsDirect

You may be asked to find an area, such as

Find the area of the triangle formed by the x-axis and the normal and tangent to the curve

at the point (0,3)

First differentiate
So the gradient of the tangent is
and the gradient of the normal is
Find the equation of the tangent
Therefore the tangent crosses the x-axis at
Now find the equation of the normal
so the normal crosses the x-axis at

We can now make a sketch, to show the area that we want,

So, we want the area of a triangle whose height is 3 and whose base length is 7.5.

So the area is 10.25