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May 14, 2025, 11:09:38 pm
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Author Topic: Normals and tangents  (Read 1625 times)  Share 

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mals22

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Normals and tangents
« on: November 06, 2012, 08:09:56 pm »
+1
Strugglinggg.
Anyone care to explain these with use of an example? How to work them out?
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b^3

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Re: Normals and tangents
« Reply #1 on: November 06, 2012, 08:17:46 pm »
+8
Lets take the function and the point as as an example.
To find the tangent we need
- the gradient at the point (using the derivative)
- the point in order to find the equation of the tangent
To find the normal we need
- the gradient at the point (using the derivative), then use , as the gradient and the normal are perpendicular to each other
- the point in order to find the equation of the normal.
So lets find the tangent at the point .
Finding the gradient, we need to find the derivative.

So at the point , we have
So .
Now to find the equation, we have the equation of a straight line,

Now for the normal, as the normal is perpendicular to the tangent, we have .
Then finding the equation, again using the equation of a straight line.

Graphed it https://www.desmos.com/calculator/mqekfqhklj
« Last Edit: November 06, 2012, 08:21:35 pm by b^3 »
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BigAl

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Re: Normals and tangents
« Reply #2 on: November 06, 2012, 08:21:01 pm »
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derive the rule and put the x value. that's your gradient at x and tangent. normal is negative reciprocal of that. when finding the equation of the tangent you need two points and use the formula y-y point=gradient(x-xpoint). from this equation you should obtain y=something. You can work other way around as well. if the equation the tangent is given just take the coefficient of x and equate that to the derived function to find out where the tangent is. and one more thing...x value is in common both original function and the tangent. hope this helps
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studynotes

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Re: Normals and tangents
« Reply #3 on: November 06, 2012, 09:28:34 pm »
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just with that last point is the x value common for the normal aswell since the normal is just perpendicular to the tangent?..

thanks
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b^3

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Re: Normals and tangents
« Reply #4 on: November 06, 2012, 09:35:00 pm »
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Quote from: studynotes on November 06, 2012, 09:28:34 pm
just with that last point is the x value common for the normal aswell since the normal is just perpendicular to the tangent?..

thanks
Yes it is -> https://www.desmos.com/calculator/mqekfqhklj
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studynotes

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Re: Normals and tangents
« Reply #5 on: November 06, 2012, 09:38:20 pm »
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thanks b^3! just with the tangents and normal what do we do if we aren't given an both the x and y point?
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b^3

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Re: Normals and tangents
« Reply #6 on: November 06, 2012, 09:43:16 pm »
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If you're given the coordinate, then you can sub the into the equation/function to get the value.

If you're given a gradient and asked to find the point where the function has a tangent with that gradient, then you find the derivative, and let that equal that gradient to find your value, and then from that you can find your value.
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mals22

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Re: Normals and tangents
« Reply #7 on: November 06, 2012, 10:14:20 pm »
0
Thankyou very much!
Quote from: b^3 on November 06, 2012, 08:17:46 pm
Lets take the function and the point as as an example.
To find the tangent we need
- the gradient at the point (using the derivative)
- the point in order to find the equation of the tangent
To find the normal we need
- the gradient at the point (using the derivative), then use , as the gradient and the normal are perpendicular to each other
- the point in order to find the equation of the normal.
So lets find the tangent at the point .
Finding the gradient, we need to find the derivative.

So at the point , we have
So .
Now to find the equation, we have the equation of a straight line,

Now for the normal, as the normal is perpendicular to the tangent, we have .
Then finding the equation, again using the equation of a straight line.

Graphed it https://www.desmos.com/calculator/mqekfqhklj
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