Math Is Fun Forum

Macy

Guest

Tangent to the the curve ...HELP !!!! please

I pulled my hair trying to figure out this question but I could not...please help me or giving some hints

At what points on the curve with equation y = 3x^3 + 14 x^2 + 3x + 8 does the tangent pass the origin?

Thanks you

xoxoxoxo

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Tangent to the the curve ...HELP !!!! please

Hi Macy;

Here is one tangent y = ( 77 / 3 ) x that passes through the origin.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Macy

Guest

Re: Tangent to the the curve ...HELP !!!! please

How do you work it out???
Derivatitve? or any other method? and they ask the coordinate of the points on the curve not the tangent equation

My

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Tangent to the the curve ...HELP !!!! please

Easy to get the points on the curve. The problem is,  that may not qualify as a tangent. It intersects the curve again at another point  in quadrant 3.

There are three possible tangent lines that pass through the origin.

y = ( 77 / 3 ) x

y = - 16 x

y = - 17 x

They are all tangent to some point on that curve but they all intersect  the function at more than one point!

Wikipedia says above that a tangent line may cross the curve at some other point or a at the point of tangency. Using that definition all three of the above straight lines are tangents that pass through (0,0)

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Macy

Guest

Re: Tangent to the the curve ...HELP !!!! please

I don't know how do you figure out the tangent equation..Please explain to me

Thx

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Tangent to the the curve ...HELP !!!! please

I hate to provide this answer because it is directly related to one of my puzzle problems that no one has solved yet.

This method because of discontinuities may not always work. The wikipedia page uses a slightly different method which you might want to explore.

1) Solve for x in the following equation:

f(-2) = 34 so your first point is (-2,34)
f(-1) = 16 so your second point is (-1,16)
f(2/3) = 154/9 so your third point is (2/3,154/9)

What do you have now? You have 3 sets of coordinates for tangent lines that pass through (0,0).

To find the tangent lines that correspond to the above points just curve fit with (0,0). Use this formula.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Tangent to the the curve ...HELP !!!! please

Hi Macy;

I have interpreted your problem as wanting tangents that pass through the origin. If you just wanted the tangent at x = 0 then that is a different thing. You use this method then:

Where a = 0:

That is the tangent of the curve at x = 0. A different question than the other one I answered in post #6.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Macy

Guest

Re: Tangent to the the curve ...HELP !!!! please

Thank you for your reply. I actually learn new method for finding the tangent to the curve.
Even though I have not fully understood why you can set f(x) = f'(x) (x - x1) + y1
Oopsss I got this now during I reply to you ....
Very very interesting way to interpreted the gradient ...

xoxoxoxo

Macy

Guest

Re: Tangent to the the curve ...HELP !!!! please

I hate to provide this answer because it is directly related to one of my puzzle problems that no one has solved yet.

This method because of discontinuities may not always work. The wikipedia page uses a slightly different method which you might want to explore.

Sorry Bobbym, I forgot to ask what is your puzzle that no one has solved yet ?. Can you post it again, see if i have some ideas for you

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Tangent to the the curve ...HELP !!!! please

Hi Macy;

The problem is located here:

http://www.mathisfunforum.com/viewtopic … 12968&p=13

Post #317.

Very very interesting way to interpreted the gradient ..

I worked it out myself to solve problems of that type. It can automated and runs in a program very easily.

Which was the question you were asking tangent at x = 0 or tangents through (0,0)?

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Macy

Guest

Re: Tangent to the the curve ...HELP !!!! please

The Tangents through (0,0). You know when we have overloaded with work our brain does not function well
Have a good weekend !

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Tangent to the the curve ...HELP !!!! please

Hi Macy;

Thanks, glad to help.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.