Differentiate with respect to .
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Differentiate with respect to .
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Find for each of the following:
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Differentiate with respect to , simplifying your answers as far as possible:
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A curve has the equation
Find the gradient of the normal to the curve at the point giving your answer correct to 3 decimal places.
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Find the equation of the tangent to the curve at the point giving your answer in the form , where and are integers.
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Let where and
Find the equation of the tangent of at
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A curve has the equation
Find expressions for and .
Determine the coordinates of the local minimum of the curve.
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The diagram below shows part of the graph of where is the function defined by
Points and are the three places where the graph intercepts the -axis.
Find
Show that the coordinates of point are
Find the equation of the tangent to the curve at point
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Let
Find
Find
Find the exact of the points of inflection for the graph of .
Find
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Let where
Find the number of points containing a horizontal tangent.
Show algebraically that the gradient of the tangent at is
State the gradient of the tangent at
It can be found that as the function, undergoes a transformation the number of stationary points found between increases.
Find the number of stationary points on after a transformation of and hence, state the general rule representing the number of stationary points in terms of where
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Let and for
Solve
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