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#1 2015-12-27 10:24:20

tyuighp
Member
Registered: 2015-12-04
Posts: 12

Find the equations

Find the equations of the tangent line to

f(x)=3x^4-4x^3

at two different points

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#2 2015-12-27 11:07:10

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Find the equations

What two points? Are they on the curve?

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.

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#3 2015-12-28 09:33:57

tyuighp
Member
Registered: 2015-12-04
Posts: 12

Re: Find the equations

hi bobbym

yes they are on the curve

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#4 2015-12-28 13:14:24

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Find the equations

What points are they?

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.

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#5 2015-12-31 10:09:57

tyuighp
Member
Registered: 2015-12-04
Posts: 12

Re: Find the equations

Find the equation of the line that touches the curve

at two different points.

Solution

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#6 2016-01-02 15:28:23

Nehushtan
Member
Registered: 2013-03-09
Posts: 918
Website

Re: Find the equations

If the equation of the tangent line is y = mx + c we have

So we want to find distinct points x=a and x=b such that

Let u = a + b and v = ab; then [3] and [4] can be expressed as

Substituting into [6]

But

We reject this since a and b must be distinct.

Hence

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#7 2016-01-02 17:25:55

Nehushtan
Member
Registered: 2013-03-09
Posts: 918
Website