The equation of a curve is
Find
The gradient of the tangent to the curve at point is .
Find
the equation of the tangent to the curve at point
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The equation of a curve is
Find
The gradient of the tangent to the curve at point is .
Find
the equation of the tangent to the curve at point
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Consider the function
Find
Find the gradient of the graph of at
Find the coordinates of the points at which the normal to the graph of has a gradient of 4.
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The equation of a curve is .
Find the equation of the tangent to the curve at
Give your answer in the form .
Find the coordinates of the points on the curve where the gradient is .
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Consider the function .
Calculate
A line, is tangent to the graph of at the point .
Find the equation of . Give your answer in the form .
The graph of and have a second intersection at point .
Use your graphic display calculator to find the coordinates of .
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Consider the function .
Find .
The equation of the tangent line to the graph at is .
Calculate the value of .
Calculate the value of and write down the function.
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The curve with equation has a gradient of 7 at the point and a gradient of 3 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 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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Find the values of for which is an increasing function.
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Show that the function is increasing for all
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The graph of the cubic function is shown below. Point a local minimum, is located at the origin and point , a local maximum, sits at the point .
State the equations of the horizontal tangent to the curve.
Write down the value of where the point of inflection is located.
Find the intervals where is decreasing.
Sketch the graph of labelling clearly any intercepts and axis of symmetry.
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The diagram below shows part of the curve with equation . The curve touches the -axis at and cuts the -axis at . The points and are stationary points on the curve.
Using calculus, and showing all your working, find the coordinates of and .
Show that is a point on the curve and explain why those must be the coordinates of point
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The equation of the curve is . A section of the curve is shown on the diagram below.
Find .
There are two points, and , along the curve at which the gradient of the normal to the curve is equal to .
Calculate the -coordinates of points and .
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Find the -coordinates of the stationary points on the graph with equation
Find the nature of the stationary points found in part (a).
Determine the -coordinate of the point of inflection on the graph with equation
Explain why, in this case, the point of inflection is not a stationary point.
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The graph of a continuous function has the following properties:
The function is concave down in the interval
The function is concave up in the interval
The graph of the function intercepts the -axis at the points and where and are such that
The coordinates of the turning points of the function are and , which are such that
The graph of the function intercepts the -axis at
Given that the value of the function is positive when , sketch a graph of the function. Be sure to label the -axis with the -coordinates of the stationary points and the point of inflection, and also to label the points where the graph crosses the coordinate axes.
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