Differentiation (Cambridge (CIE) IGCSE Maths: Extended)

A curve has the equation  

Work out the coordinates of the two turning points.

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

Determine whether each of the turning points is a maximum or a minimum. Give reasons for your answers.

A curve has equation .

i) Find the coordinates of the two stationary points.  

( .................... , .................... ) and ( .................... , .................... ) [5]

ii) Determine whether each of the stationary points is a maximum or a minimum. Give reasons for your answers.  

[3]

A curve has equation .

Find the coordinates of the two turning points.  

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

Determine whether each of the turning points is a maximum or a minimum.

Give reasons for your answers.

The curve has equation where and are constants.

The point with coordinates (2, –6) lies on .

The gradient of the curve at is 16.

Find the coordinate of the point on the curve whose coordinate is 3.

Show clear algebraic working.

Part of the graph with equation  is shown below.

The graph has three stationary points, indicated on the graph by points P , Q and R. Find the area of the triangle PQR.

The curve  has equation .

Find  .

    = ..............................................

There are two points on the curve  at which the gradient of the curve is .

Find the  coordinate of each of these two points. Show clear algebraic working.