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Calculus Continued

Tangents and Normals Example Find the equations

of the tangent and normal to the graph of at the

point where

Example Find the equation of the tangent and the

normal to the curve at the point A

where

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

Stationary points will be one of the following

types

Points of inflection

Maximum point

Minimum point

Example Find the stationary points to the graph

of . Hence sketch the graph of

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.

Maximum

Minimum

Inflections

Example Obtain the stationary point and determine

type of the graph of

Example Obtain the stationary point and determine

type of the graph of

Example Find the maximum and minimum values of y

when Hence sketch the graph of

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