1. S TARTER – W RITE FINAL ANSWER ON WHITEBOARD ! Write an equation of the line that passes through the points (-1, 0) and (5, 2). Leave answer in the form y = mx + c. S OLUTION :

2. T ANGENT & N ORMAL L INES D IFFERENTIATION AS Maths with Liz

3. G OALS Writing equations of tangents and normals using differentiation Recalling the equation of a line in the form Finding the gradient function

4. I MPORTANT TERMS A tangent to a curve is a straight line which touches the curve at a single given point. A normal to a curve is a straight line that is perpendicular to the tangent at a single given point. If gradient of tangent = then gradient of normal =

5. E XAMPLE 1 Find the equation of the tangent to the curve at the point where. Solution: Remember, the tangent is a straight line, so what do we need to write the equation of a line? the gradient & a point if we’re using the form Start by finding the gradient function: at So, gradient, m = 6

6. E XAMPLE 1 ( CONT ’ D …) Next, find a point. Since we know the tangent exists at the point, let’s substitute this into the original equation to find it’s y coordinate. So, gradient, m = 6 So, point is ( 1, 5) Bring everything together to write the equation: The equation of the tangent where is.

7. Y OU TRY ! Find the equation of the tangents to the curves at the given points. (a) (b) (c) at

8. S OLUTIONS Find the equation of the tangents to the curves at the given points. (a) (b) (c) at

9. E XAMPLE 2 Find the equation of the normal to the curve at the point where. Start by finding the gradient of the tangent: at Gradient of tangent, Solution: Gradient of normal, Find a point: So, point is ( 3, 4)

10. The equation of the normal where is. E XAMPLE 2 ( CONT ’ D...) Bring everything together to write the equation: Gradient of normal, Point is (3, 4) OR

11. Y OU TRY ! Find the equation of the normals to the curves at the given points. (a) (b) (c) at

12. S OLUTIONS Find the equation of the normals to the curves at the given points. (a) (b) (c) at

13. I NDEPENDENT S TUDY Mymaths Tangents & Normals: Exam Style Questions (slides 6 & 7)Tangents & Normals Mymaths Tangents & Normals: Online HomeworkOnline Homework Please copy, complete, & mark all questions in your notebook in a colourful pen. DUE TUESDAY, NOVEMBER 4 TH