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

Find the equations of the tangent line to

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

at two different points

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

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

hi bobbym

yes they are on the curve

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

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

Find the equation of the line that touches the curve

at two different points.Solution

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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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