Differentiate .
Find the coordinates of the turning point of the graph of .
( ...................... , ...................... )
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Differentiation
Differentiate .
Find the coordinates of the turning point of the graph of .
( ...................... , ...................... )
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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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On the diagram, sketch the graph of .
Show the values of the intersections with the axes.
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Expand and simplify.
is the point
.
The tangent to the graph of at
meets the
-axis at
.
Find the coordinates of .
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Find the two stationary points on the graph of
( ..................... , ..................... )
( ..................... , ..................... )
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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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.
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 .
i) Differentiate
[2]
ii) Find the equation of the tangent to the curve at the point (2, 6).
[3]
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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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