Differentiate
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Differentiate
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Write down the gradient of the line with equation , where is a constant.
Find the gradient at the point where for the following functions
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Given that , find .
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Find the -coordinate of the point on the curve where the gradient is 4.
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Find the coordinates of the points on the curve where the gradient is 0.
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Find when .
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The function is given by
.
Show that can be written in the form , where a, b, c and d are constants to be found.
Find
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Find an expression for when .
Find the gradient of at the points where
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For the graph with equation , find the gradient of the tangent at the point where .
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For each of the following, find in terms of x:
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Given that find .
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For each of the following, find in terms of x:
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The function f is defined by .
Find .
Solve the equation .
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A curve has the equation .
Find .
Find the coordinates of the point on the curve where the gradient is 2.
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The function f is defined by .
Find
Given that the equation has exactly one real solution, find the value of c.
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A curve is described by the equation
Make y the subject of the equation.
Hence find
Find the coordinates of the point on the curve where the gradient is .
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The curve with equation has a gradient of at the point and a gradient of at the point .
By considering show that and
Hence find the values of and .
By considering a point that you know to be on the curve, find the value of .
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The curve has equation
Show that the point lies on .
Show that the value of at is 16.
Find an equation of the tangent to at .
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The curve has equation The point lies on .
Find an expression for .
Show that an equation of the normal to at point is .
This normal cuts the -axis at the point .
Find the length of , giving your answer as an exact value.
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Given that , find
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For each of the following, find in terms of :
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Given that find
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For each of the following, find in terms of :
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The function is defined by Show that there are no solutions to the equation
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A curve has the equation
Show that where and are rational numbers to be found.
Hence find the coordinates of the point on the curve where the gradient is 0.
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A curve has the equation where is a constant. Given that there is only one point on the curve where the gradient is zero, determine the possible values of .
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A curve is described by the equation .
By rearranging the equation to make the subject, find .
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The curve with equation has a gradient of 8 at the point , and a gradient of at the point . Find the values of and .
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The curve has equation The point lies on .
Find an equation of the tangent to at .
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The curve has equation The point lies on .
The normal to at intersects the -axis at the point .
Find the coordinates of .
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Given that , find
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For each of the following, find in terms of x :
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Given that , find
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For each of the following, find in terms of :
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A curve has the equation . Find the coordinates of the point on the curve where the gradient is 0.
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The function f is defined by Determine the relationship between the value of and the number of real solutions to the equation .
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A curve is described by the equation Find
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The curve with equation passes through the point . At the point the gradient of the curve is 7. Find the values of and .
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A curve has equation .
A is the point on the curve with coordinate 0, and is the point on the curve with coordinate 6.
is the point of intersection of the tangents to the curve at and .
Find the coordinates of point .
Calculate the area of triangle .
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A curve is described by the equation , where
is the point on the curve such that the normal to the curve at also passes through the origin.
Find the coordinates of point . Give your answer in the form , where a and b are rational numbers to be found.
Write down the equation of the normal to the curve at .
Show that an equation of the tangent to the curve at is
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