1. Calculus Continued Tangents and Normals Example Find the equations of the tangent and normal to the graph of at the point where

2. Example Find the equation of the tangent and the normal to the curve at the point A where

3. Stationary Points Stationary Points on the graph of a function are points at which the gradient is zero. Hence to obtain coordinates of stationary points on the graph of 1. Solve -gives the x coordinates then 2. Substitute in -gives the y coordinates

4. Stationary points will be one of the following types: Minimum point Maximum point Points of inflection

5. Example Find the stationary points to the graph of. Hence sketch the graph of

6. For type? We can determine type of any stationary point by looking at the change in its gradient as we go ‘through’ the stationary point. – Minimum + + – Maximum

7. + + – – Inflections

8. Example Obtain the stationary point and determine type of the graph of

9. Example Obtain the stationary point and determine type of the graph of

10. Example Find the maximum and minimum values of y when Hence sketch the graph of