A curve has the equation .
Find an expression for .
Did this page help you?
A curve has the equation .
Find an expression for .
Did this page help you?
Find for
Did this page help you?
The curve with equation passes through the point with coordinates (-3 , 1).
Did this page help you?
Differentiate with respect to x.
Differentiate with respect to x.
Did this page help you?
Differentiate with respect to x
Differentiate with respect to .
Did this page help you?
Write down when
Did this page help you?
The function is defined as
Show that the graph of intercepts the x-axis at the points (1 , 0) and (2 , 0).
Find .
Find the gradient of the tangent at the point (1 , 0).
Hence find the equation of the tangent at the point (1 , 0), giving your answer in the form , where a, b and c are integers to be found.
Did this page help you?
A curve has the equation
Find the gradient of the normal to the curve at the point , giving your answer correct to 3 decimal places.
Did this page help you?
Find for each of the following:
Find for each of the following:
Did this page help you?
Find the equation of the tangent to the curve at the point , giving your answer in the form, where a, b and c are integers.
Did this page help you?
Differentiate with respect to x, simplifying your answers as far as possible:
Did this page help you?
Differentiate with respect to x.
Did this page help you?
Show that if , then
Hence find the gradient of the tangent to the curve at the point with coordinates
Did this page help you?
The diagram below shows part of the graph of , whereis the function defined by
Points A, B and C are the three places where the graph intercepts the x-axis.
Find .
Show that the coordinates of point A are (-2, 0).
Find the equation of the tangent to the curve at point A.
Did this page help you?
A curve has the equation
Show that the equation of the tangent to the curve at the point with x-coordinate 1 is
Did this page help you?
For , where is a real number and is an integer, show that
Did this page help you?
Find the gradient of the normal to the curve at the point with x-coordinate 0. Give your answer correct to 3 decimal places.
Did this page help you?
Differentiate with respect to x, simplifying your answers as far as possible:
Did this page help you?
By writing as and then using the product and chain rules, show that
Did this page help you?
Given that ,
Find in terms of y
Hence find in terms of x.
Did this page help you?
The diagram below shows part of the graph of , where is the function defined by
Point A is a maximum point on the graph.
Show that the x-coordinate of A is a solution to the equation
Did this page help you?
A curve has the equation .
Show that the gradient of the normal to the curve at the point is
Did this page help you?
Find the derivative of the function
Did this page help you?
Show that the derivative is
Hence find the equation of the tangent to the curve at the point , giving your answer in the form , where a and b are to be given as exact values.
Did this page help you?
Differentiate with respect to x, simplifying your answers where possible:
Did this page help you?
The diagram below shows the graph of , where is the function defined by
The points A and B are maximum and minimum points, respectively.
Find the difference between the y-values of the coordinates of A and B, giving your answer correct to 3 decimal places.
Did this page help you?
A is the point on the graph of such that the tangent to the graph at passes through the point . Show that the x-coordinate of A satisfies the equation
Did this page help you?
A sequence of functions is defined by the recurrence relation
Based on that sequence, the functionis defined by
Calculate the value of
Did this page help you?