Differentiation (Cambridge (CIE) IGCSE Maths: Extended)

On the diagram, sketch the graph of  .
Show the values of the intersections with the axes. 

Expand and simplify.

is the point .
The tangent to the graph of  at  meets the -axis at .

Find the coordinates of .

Find the two stationary points on the graph of  

( ..................... , ..................... )
( ..................... , ..................... )

A curve has equation .

Work out the coordinates of the two stationary points.

( .................... , ....................)
( .................... , ....................)

Determine whether each stationary point is a maximum or a minimum. Give reasons for your answers.

.

Find .

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The curve with equation  has two stationary points.

Work out the coordinates of these two stationary points.

 The diagram shows a sketch of the curve  .

i) Differentiate 

   [2]

ii) Find the equation of the tangent to the curve at the point (2, 6). 

 [3]

, where  is the derived function.  

Find the value of  and the value of .  

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A curve, C, has equation  where k is a constant.

Show that when k = 0, the turning point on C has coordinates (0, -3).

Show that when , the turning point on C must have a negative x-coordinate.

When  determine whether or not the -coordinate of the turning point is negative.