1. the gradient is 0

2. Differentiation – Tangents & Normals
Know what tangents and normals to curves are.
Understand the process for finding a tangent to a curve at a particular point given the curves equation and an x value.
Be able to explain how the process must be altered to find the equation of the normal to the curve.

3. What is a tangent?
We just learnt the gradient function that allows us to find the gradient at any point of a curve. If we have a gradient, and a point, we can find a line equation! Tangents are the line equations from this. These just touch the curve at the point you’re looking for.

4. Process of finding a tangent
Example: Find the equation of the tangent to the curve y=f(x) given that f(x)=x3-x2+3x when x=2 Step 1) Find point for line. At x = 2, or y = f(2)

5. Process of finding a tangent
Example: Find the equation of the tangent to the curve y=f(x) given that f(x)=x3-x2+3x when x=2 Step 2) Find gradient via differentiation

6. Process of finding a tangent
Example: Find the equation of the tangent to the curve y=f(x) given that f(x)=x3-x2+3x when x=2 Step 3) Use m & point with line equation

7. What is a normal?
A normal is a line at right angles to the tangent, crossing at the same point on the curve.

8. Process of finding a normal
Example: Find the equation of the Normal to the curve y=2x3-3x2+5x-1 at the point where x=1 Step 1) Find point for line. At x = 1, or y = f(1)

9. Process of finding a normal
Example: Find the equation of the Normal to the curve y=2x3-3x2+5x-1 at the point where x=1 Step 2) Find gradient via differentiation. Normal is the perpendicular gradient to this!

10. Process of finding a normal
Example: Find the equation of the Normal to the curve y=2x3-3x2+5x-1 at the point where x=1 Step 3) Use m2 & point with line equation

11. Independent Study
Misc. exercise 5 p90 pretty tough questions (solutions p420)