1. Chapter 9 & 10 Differentiation Learning objectives: 123 DateEvidenceDateEvidenceDateEvidence Understand the term ‘derivative’ and how you can find gradients of curve / Use differentiation to find the gradient of a curve at any point on a curve / / Find the equation of the tangent and normal to a curve at any given point / / / Appreciate that derivatives represent rates of change / / / Understand how derivatives can tell you whether a function is increasing or decreasing / / /

2. 1. Differentiation

3. EG3. (a) Find the gradient of the curve y = 3x – 8x 2 at the point P ( 3, -63 ). (b) Find the gradient of the curve y = 4x 3 + 20x 2 at the point Q where x = -2. 2. Finding gradients at specific points on a curve The gradient of a curve at any point P is equal to the gradient of the tangent to the curve at P. We use differentiation method to find the gradient. In order to find the gradient at a particular point on the curve: Step 1: differentiate the equation of the curve; Step 2: Substitute into the derivative the x-coordinate of the point at which we need the gradient.

4. 3. Finding points on a curve with a given gradient

5. 4. Simplifying expression before differentiation

6. 5. The equation of a tangent to a curve

7. 6. The equation of a normal to a curve

8. 7. Rates of change

10. 7. Increasing and decreasing functions