Maths with Lemon

Tangents and Normals

" Two tangents meet at a bar. After a long evening the one tangent says: "That was fun, we should meet again!" The other: "You know that isn't going to happen!" "

Anonymus

Tangents and Normals

What you have to know:

Differentiate all the basic functions.
(If not, check this lesson)
The general form of a line.
(If not, check this lesson)
You must be able to manipulate exponential expressions.
(If not, check this lesson)
You must be able to manipulate logarithmic expressions.
(If not, check this lesson)

Key Points

1. Watch the video:

2. Check out this presentation.

Old-school style explanation of a tangent!

What you have to know:

How to calculate area.

Key Points

1. Watch the video:

Extra

Material and references:

Hodder Book SL(ISBN: 9781510462359) :
9D

Key Points

1. Old-school style explanation of a tangent!

2. You should be able to find the equations of the tangent and normal to a function at a given point. The equation of the tangent to the curve \( y = f(x) \) at the point where \( x = a \) is \[ y - y_1 = m(x - x_1), \] where \( m = f'(a) \), \( x_1 = a \), and \( y_1 = f(a) \).

3. The equation of the normal to the curve \( y = f(x) \) at the point where \( x = a \) is \[ y - y_1 = m(x - x_1), \] where \( m = -\frac{1}{f'(a)} \), \( x_1 = a \), and \( y_1 = f(a) \).

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