Help me find the co-ords of Q please!

OK, I am completely lost - help please!!!

The curve C has the equation 1/3x^3 - 4x^2 + 8x + 3

The point P lies on C at (3,0), and the equation of the tangent to C at P is (by my working) y=21-7x

Another point Q also lies on C. The tangent to C at Q is parallel to the tangent to C at P.

Find the co-ordinates of Q.

PLEASE help me out - I have no idea where to start!

Thanks guys :smile:

Reply 1

Calira

If it's parallel to the line y=21-7x, you know it'll have gradient of -7; so will have the equation y=K-7x for some constant K

Reply 2

Milch

14

Toffee_Kid

OK, I am completely lost - help please!!!

The curve C has the equation 1/3x^3 - 4x^2 + 8x + 3

The point P lies on C at (3,0), and the equation of the tangent to C at P is (by my working) y=21-7x

Another point Q also lies on C. The tangent to C at Q is parallel to the tangent to C at P.

Find the co-ordinates of Q.

PLEASE help me out - I have no idea where to start!

Thanks guys :smile:

My friend.
As it is parallel it has the same gradient of -7
Now find the derivitive of the curve. (find dy/dx of it) and equal this to -7
Now solve this equation to find x
Sub x in the original equation to find y and there are your coordinates!

Reply 3

Rodelero

Differentiate the curve. Find answers for dy/dx = -7. One of them will be the x-coord of point P, the other point Q (the one which isn't x=3)

Then, put this value of x through the equation of the curve. You then have the y-coordinate, and x-coordinate. Bingo!

Reply 4

Milch

14

Yes I have done it myself and it works. If you need the answer then just shout. I hope my advice has helped you.

Reply 5

Khodu

19

Milch

My friend.
As it is parallel it has the same gradient of -7
Now find the derivitive of the curve. (find dy/dx of it) and equal this to -7
Now solve this equation to find x
Sub x in the original equation to find y and there are your coordinates!

What I'd do...

A few past papers that I did a while back only asked for the x-coordinates... I realised that after finding an ugly y coordinate with fractions that you don't need ... Prefer my answers to be in the form (x,y) tbh...