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How to find the coordinates where a tangent touches a curve?

- Professor Tim

Posted by Professor Tim on Nov 17, 2009 in Answer This If You Can! | 1 comment

I’d similar to to know how to find where a following equations touch:

y= -3x + 2
y= x^3 + x^2 – 4x + 1

Thanks allot!

^=to a energy of.

Community Answers

11-17-09
Morningfox says:
They touch where the two y’s are equal
y = -3x + 2 = x^3 + x^2 – 4x + 1
Subtract -3x +2 from both sides, to get
0 = x^3 + x^2 – 4x + 1 +3x – 2
0 = x^3 + x^2 – x -1
Solving that, we get:
0 = (x+1)^2 (x-1)
The roots are:
x = -1, y = 5 (tangent point to -3x +2)
and
x = +1, y = -1
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