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

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Presentation transcript:

© Annie Patton Implicit Functions Next Slide

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

© 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

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

© 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

© 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

© 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.

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

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

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

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

© 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.

© 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.