1. Applying Differentiation
Differentiation Lesson 2
Chapter 7

2. Applying Differentiation
Last lesson we learned that you can find the gradient of a function by differentiating it

3. Applying Differentiation
This lesson you are going to apply your knowledge of differentiation to be able to find the value of the gradient at any point on a curve

4. Example 1 Find the gradient of y = f(x) at the point (½, 0)
Find the coordinates of the point on the graph of y = f(x) where the gradient is 8
Find the gradient of y = f(x) at the points where the curve meets the line y = 4x – 5

5. Example Find the gradient of y = f(x) at the point (½, 0)
Find the coordinates of the point on the graph of y = f(x) where the gradient is 8
Find the gradient of y = f(x) at the points where the curve meets the line y = 4x – 5

6. Example Find the gradient of y = f(x) at the point (½, 0)
Find the coordinates of the point on the graph of y = f(x) where the gradient is 8
Find the gradient of y = f(x) at the points where the curve meets the line y = 4x – 5

7. Finding the gradient Next page Complete the table.
Find the gradient of each function at the specified point.

8. Differentiation and Coordinate Geometry
Rewind back to Chapter 5….
You learned coordinate geometry for this purpose!!!

9. Question 1 The equation of a curve is
Find the gradient of the tangent and of the normal to the curve at the point
(-2, 4)

10. Question 2 Find the coordinates of the points on the curve
where the gradient is 4.

11. Example