Differentiate .
Find the coordinates of the turning point of the graph of .
( ...................... , ...................... )
Did this page help you?
Syllabus Edition
First teaching 2021
Last exams 2024
Differentiate .
Find the coordinates of the turning point of the graph of .
( ...................... , ...................... )
Did this page help you?
Calculate the gradient of at .
Did this page help you?
Use differentiation to find for the following:
.
Did this page help you?
For the curve with equationÂ
findÂ
find the coordinates of the point on the curve where the gradient is 2.
Did this page help you?
A curve has equationÂ
FindÂ
Find the gradient of the curve at the point where:
(i)Â Â Â
[2]
(ii)Â Â
[2]
What can you say about the tangents to the curves at these two points?
Did this page help you?
A curve has the equation Â
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.
Did this page help you?
Find the two stationary points on the graph of
Â
( ..................... , ..................... )
( ..................... , ..................... )
Did this page help you?
A curve has equation .
i)
Find the coordinates of the two stationary points.
Â
( .................... , .................... ) and ( .................... , .................... ) [5]
ii)
Determine whether each of the stationary points is a maximum or a minimum.
Give reasons for your answers.
Â
[3]
Did this page help you?
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.
Did this page help you?
A curve has equation .
Find the coordinates of the two turning points.
Â
(............ , ............) and (............ , ............)
Determine whether each of the turning points is a maximum or a minimum.
Give reasons for your answers.
Did this page help you?
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.
Did this page help you?
.
Find .
....................................
The curve with equation has two stationary points.
Work out the coordinates of these two stationary points.
Did this page help you?
 The diagram shows a sketch of the curve .
Did this page help you?
, where is the derived function.
Â
Find the value of and the value of .
Â
................................................
................................................
Did this page help you?
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.
Did this page help you?
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.
Did this page help you?
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.
Did this page help you?