1. Differentiation The original function is the y- function – use it to find y values when you are given x Differentiate to find the derivative function or ‘gradient’ function Use this to find the value of the gradient at any point x on the curve E.g. When

3. Gradient of a point or gradient of a tangent?

4. The equation of the tangent to a curve at a given point Find the equation of the tangent to the curve when x=3 Step 1: differentiate the function to get the gradient function Step 2: find the gradient of the tangent (i.e. the curve) when x=3 Step 3: find the y-coordinate when x=3 Step 4: Find the equation of the tangent (this is a straight line equation!) The Equation of a Tangent or of a Normal

5. 1. Tangents a) b) 2. 3. Extension

6. 1. 2. 3. 6 The Equation of a Tangent or of a Normal

7. Extension 7 The Equation of a Tangent or of a Normal

8. What is ‘normal’ in a Maths lesson?

9. The equation of the normal to a curve at a given point Find the equation of the normal to the curve at the point where x is -1 Step 1: differentiate the function to get the gradient function Step 2: find the gradient of the tangent (i.e. the curve) when x= -1 Step 4: find the y-coordinate when x= -1 Step 5: Find the equation of the normal (this is a straight line equation!) Step 3: find the gradient of the normal when x= -1 9 The Equation of a Tangent or of a Normal

10. Normals 10 The Equation of a Tangent or of a Normal

11. Gradient of a Curve Investigating further Copy this curve onto your whiteboard. Mark on to the graph where it has a positive gradient. Mark where it has a negative gradient If y stands for the distance travelled by a car and x stands for time, when is the car stationary?