Calculus Continued

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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
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Example Find the equation of the tangent and the
normal to the curve at the point A
where
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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
 
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Stationary points will be one of the following
types
Points of inflection
Maximum point
Minimum point
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Example Find the stationary points to the graph
of . Hence sketch the graph of
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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
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Inflections
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Example Obtain the stationary point and determine
type of the graph of
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Example Obtain the stationary point and determine
type of the graph of
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Example Find the maximum and minimum values of y
when Hence sketch the graph of