# Numbers | Maths with Lemon

Source: https://mathswithlemon.io/aa-calculus-tangen%20normal.html


## 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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