A tangent is a line that touches the curve.

A normal is a line that is perpendicular to the normal.

Remember this formula:

(gradient of tangent) x (gradient of normal) = -1

How to find gradient of tangent at x = a?

1) Differentiate y (find dy/dx)

2) substitute x = a into dy/dx to find gradient of tangent.

How to find gradient of normal at x = a?

1) Differentiate y (find dy/dx)

2) substitute x = a into dy/dx to find gradient of tangent.

3) find gradient of normal by using the following formulae: -1 / (gradient of tangent)

How to find equation of tangent at x = a?

1) Differentiate y (find dy/dx)

2) substitute x = a into dy/dx to find gradient of tangent. Let's call it m1.

3) substitute x into the y equation, to get a y value. Let's call this y value y1.

4) equation of equation : y -y1 = m1(x-a)

How to find equation of tangent at x = a?

1) Differentiate y (find dy/dx)

2) substitute x = a into dy/dx to find gradient of tangent. Let's call it m1.

3) substitute x into the y equation, to get a y value. Let's call this y value y1.

4) equation of equation : y -y1 = m1(x-a)

How to find equation of normal at x = a?

1) Differentiate y (find dy/dx)

2) substitute x = a into dy/dx to find gradient of tangent. Let's call it m1.

3) Find gradient of normal by using the formula gradient of normal = -1/ (gradient of tangent).

Let's call this gradient of normal m2.

3) substitute x into the y equation, to get a y value. Let's call this y value y1.

4) equation of equation : y -y1 = m2(x-a)