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#1 2007-12-01 14:20:30
- sarah.nz
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- Registered: 2007-11-30
- Posts: 3
differentiation.
The curve y=x² -3x -4 cross the x-axis at P and Q. The tangents to the curve at P and Q meet at R. The normals to the curve at P and Q meet at S. Find the distance RS.
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#2 2007-12-01 22:22:18
- Daniel123
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- Registered: 2007-05-23
- Posts: 663
Re: differentiation.
I don't have time to actually do the question, but here are the steps you need to take in order to do it:
1. Substitute y = 0 into the equation for your curve and then factorise to find the two points P and Q where it crosses the x-axis.
2. Differentiate the equation to find the gradient function
3. Substitute your two values P and Q into the gradient function to find the gradient of the tangents to the curve at those points
4. Use
to find the equations of the tangents.5. Set them equal to each other to find the co-ordinates where they cross (point R)
6. Use
to find the gradients of the normals to the curve at P and Q.7. Again use
to find the equations of the normals.8. Set them equal to each other to find the co-ordinates where they cross (point S)
9. You now have the two points R and S. Use Pythagoras to find the distance between them.
Last edited by Daniel123 (2007-12-01 22:25:58)
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#3 2007-12-02 01:18:40
- JaneFairfax
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- Registered: 2007-02-23
- Posts: 6,868
Re: differentiation.
9. You now have the two points R and S. Use Pythagoras to find the distance between them.
It will be much simpler than that. RS is actually going to be a vertical line. (I can visualize that by symmetry the two tangents and the two normals will intersect at the same x-value.) 
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#4 2007-12-02 01:35:50
- Daniel123
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- Registered: 2007-05-23
- Posts: 663
Re: differentiation.
Aah of course, I didn't think.
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#5 2007-12-02 02:21:49
- luca-deltodesco
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- Registered: 2006-05-05
- Posts: 1,470
Re: differentiation.
Aah of course, I didn't think.
no you didn't think 
The Beginning Of All Things To End.
The End Of All Things To Come.
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#6 2007-12-02 03:17:12
- mathsyperson
- Moderator
- Registered: 2005-06-22
- Posts: 4,900
Re: differentiation.
Yeah well, it doesn't really matter.
There's nothing wrong with squaring and rooting your answer to celebrate finishing. 
Why did the vector cross the road?
It wanted to be normal.
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#7 2007-12-02 17:02:56
- sarah.nz
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- Registered: 2007-11-30
- Posts: 3
Re: differentiation.
thank you guys, much help
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