Find pt where y=x^3-3x+4, y=3(x^2-x) have common tangent

[sunnshyne411]

I am not really sure how to apporach this problem. I think that you find the derivative of each of the equations.

Find the point where the curves y = x^3 − 3x + 4 and y = 3 (x^2 − x) are tangent to each other, that is, have a common tangent line.

Step 1:
Find the derivative of each equation.
y' = 3x^2 - 3 and y' = 6x - 1

I am not sure how to approach this at this point.

Please help!

 

[royhaas]

If two curves have a common tangent, they must have a common point, and their derivatives must match at the x-coordinate of that point.