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A-Level Differentiation Question (i think)

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    The Curve y= (10/2x+1) -2 intersects the x-axis at A, The tangent to the curve at A intersects the y-axis at C.

    i) Show that the equation of AC is 5y + 4x = 8
    ii) Find the distance AC

    do i differentiate it twice?
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    Have you found the point A? Have you found the equation of the tangent?

    You need to say where you're up to in the question or I can only guess why you're stuck.
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    i just differentiate y and got stuck there
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    (Original post by Candit)
    The Curve y= (10/2x+1) -2 intersects the x-axis at A, The tangent to the curve at A intersects the y-axis at C.

    i) Show that the equation of AC is 5y + 4x = 8
    ii) Find the distance AC

    do i differentiate it twice?
    The equation you have written is ambiguous.

    Do you mean  \displaystyle y = \frac{10}{2x+1} - 2 \ ?
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    yes
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    (Original post by Candit)
    The Curve y= (10/2x+1) -2 intersects the x-axis at A, The tangent to the curve at A intersects the y-axis at C.

    i) Show that the equation of AC is 5y + 4x = 8
    ii) Find the distance AC

    do i differentiate it twice?
    Part (a),

    Set y=0, to find the x-coordinate of A.
    Differentiate y = 10/(2x+1) -2 and sub in the x-coordinate of A, to get the gradient at A.
    Use the coordinates of A and the gradient obtained to find the equation of tangent at A.
    Set x=0 in the equation of tangent at A, to find the y-coordinate of point C.

    Now find the gradient of AC, by using  m = \dfrac{y_2 - y_2}{x_2 - x_1} , then form an equation.
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    umm ok get it thanks alot

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Updated: June 10, 2012
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