1. © Annie Patton Implicit Functions Next Slide

2. © Annie Patton Aim of Lesson Next Slide To establish, what is an Implicit Function and how to differentiate one.

3. © Annie Patton Implicit Functions In functions like y=x 2 +2x +3, y is expressed in terms of x. This is called an Explicit Function. In functions like x 2 +4xy –y 2 =2x, y is not expressed in terms of x. This is called an Implicit Function. Next Slide

4. © Annie Patton Differentiate x 2 +4xy –y 2 =2x with respect to x. Next Slide

5. © Annie Patton Method Differentiate each term with respect to x. Bring all the terms with to one side. Find, in terms of x and y. Next Slide

6. © Annie Patton Find the equation of the tangent to the curve 3x 2 +y 2 =28 at the point (2,-4) Next Slide Leaving Certificate Higher No 7(b) (1) Paper 1 2007

7. © Annie Patton Find the equation of the tangent to the curve 3x 2 +y 2 =28 at the point (2,-4) continued Next Slide Start clicking when you want to see the answer.

8. © Annie Patton Next Slide Start clicking when you want to see the answer.

9. © Annie Patton Leaving Certificate Higher No 7(b) (ii) Paper 1 2003 Next Slide Start clicking when you want to see the answer.

10. © Annie Patton Next Slide Start clicking when you want to see the answer.

11. © Annie Patton Next Slide Start clicking when you want to see the answer.

12. © Annie Patton A 20m ladder leans against a wall. The top slides down at the rate of 4 m/sec. How fast is the bottom of the ladder moving, when it is 16m from the wall? 20 y x Next Slide Start clicking when you want to see the answer.

13. © Annie Patton Implicit Functions In functions like y=x 2 +2x +3, y is expressed in terms of x. This is called an Explicit Function. In functions like x 2 +4xy –y 2 =2x, y is not expressed in terms of x. This is called an Implicit Function.