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C1 - How do you know when to reciprocal the gradient depending on the questions ?

Hi

I'm doing some C1 papers and was just wondering in some questions I think you have to reciprocal the gradient when actually you dont....

Just wondering is there a way of telling how depending on the question ?
Original post by User32432432
Hi

I'm doing some C1 papers and was just wondering in some questions I think you have to reciprocal the gradient when actually you dont....

Just wondering is there a way of telling how depending on the question ?


Suppose you have found the gradient of a curve, m, at a particular point.

Now, if you're working out the equation for the normal, the gradient you want is

−1m-\dfrac{1}{m}
Reply 2
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User32432432
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Original post by Indeterminate
Suppose you have found the gradient of a curve, m, at a particular point.

Now, if you're working out the equation for the normal, the gradient you want is

−1m-\dfrac{1}{m}


Do you only reciprocal when asked for e.g equation of the normal ?
Original post by User32432432
Hi

I'm doing some C1 papers and was just wondering in some questions I think you have to reciprocal the gradient when actually you dont....

Just wondering is there a way of telling how depending on the question ?


Basically if you want to find the gradient of a line perpendicular to another line, you would divide that lines gradient by -1 (i.e negative reciprocal) to find the gradient of the perpendicular line :smile:


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Original post by User32432432
Do you only reciprocal when asked for e.g equation of the normal ?


Yes, and it's important to do the negative reciprocal, not just the reciprocal.

Remember that the normal to a curve at a point is perp. to the tangent at that point. So, given the gradient of one, you can find the other :smile:
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Dualcore
Well when you differentiate you get an equation that describes the gradient at any point on the curve, this will be the gradient of the tangent at the point, so you'll only need to the reciprocal thing when it asks you for the normal.
Reply 6
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Sookiee
Basically, if the question ask for the equation of the TANGENT, use the gradient as it is. If the question ask for the equation of the NORMAL, use the negative reciprocal
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User32432432
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Original post by Sookiee
Basically, if the question ask for the equation of the TANGENT, use the gradient as it is. If the question ask for the equation of the NORMAL, use the negative reciprocal


what about perpendicular ?
Original post by User32432432
what about perpendicular ?


The normal is the perpendicular to the tangent.
Reply 9
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User32432432
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Original post by ghostwalker
The normal is the perpendicular to the tangent.

So you dont have to reciprocal it, ?
Original post by User32432432
So you dont have to reciprocal it, ?


You take the negative reciprocal of the tangent to get the gradient of the normal.

A perpendicular is perpendicular to something.
You take the negative reciprocal of the something to get the gradient of the perpendicular.

If the something is the tangent, then the perpendicular and the normal are one and the same, and you take the negative reciprocal of the tangent to find its gradient.
thank you



Original post by Dualcore
Well when you differentiate you get an equation that describes the gradient at any point on the curve, this will be the gradient of the tangent at the point, so you'll only need to the reciprocal thing when it asks you for the normal.

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