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A-Level Differentiation Question (i think)

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?
Reply 1
Avatar for Notnek
Notnek
21
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.
Reply 2
Avatar for Candit
Candit
OP
i just differentiate y and got stuck there
Reply 3
Avatar for raheem94
raheem94
13
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 y=102x+1−2 ? \displaystyle y = \frac{10}{2x+1} - 2 \ ?
Reply 4
Avatar for Candit
Candit
OP
yes
Reply 5
Avatar for raheem94
raheem94
13
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=y2−y2x2−x1 m = \dfrac{y_2 - y_2}{x_2 - x_1} , then form an equation.
(edited 11 years ago)
Reply 6
Avatar for Candit
Candit
OP
umm ok get it thanks alot

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