Differentiate .
Find the coordinates of the turning point of the graph of .
( ...................... , ...................... )
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Syllabus Edition
First teaching 2021
Last exams 2024
Differentiate .
Find the coordinates of the turning point of the graph of .
( ...................... , ...................... )
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Calculate the gradient of at .
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Use differentiation to find for the following:
.
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For the curve with equation
find
find the coordinates of the point on the curve where the gradient is 2.
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A curve has equation
Find
Find the gradient of the curve at the point where:
(i)
[2]
(ii)
[2]
What can you say about the tangents to the curves at these two points?
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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.
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Find the two stationary points on the graph of
( ..................... , ..................... )
( ..................... , ..................... )
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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]
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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.
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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.
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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.
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.
Find .
....................................
The curve with equation has two stationary points.
Work out the coordinates of these two stationary points.
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The diagram shows a sketch of the curve .
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, 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.
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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.
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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.
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