A tangent line to both functions

[Atran]

Homework Statement

Determine a line that is tangent to both f(x)=x² and g(x)=x²-2x

Homework Equations

The Attempt at a Solution

f(x)=x² => f'(x)=2x
g(x)=x²-2x => g'(x)=2x-2

f'(a) = f'(b)
2a = 2b-2

I don't know how to continue.
Thanks for help.

 

[mfb]

If h(x) is that line, what do you know about h(a), h(b)?

 

[Atran]

Thank you.

h(b) = (2b-2)b+c => c = -b²

h(a) = (2b-2)a+c = (2b-2)a-b² => (a-b)²+2a=0
2a = 2b-1 => a = b-1
(-1)²+2a=0 => a=-0.5 and b=0.5

 

[mfb]

2a = 2b-1 => a = b-1

That is not true, but I think you mean 2(b-1).
The result is right.

 

[Atran]

Yes, I meant 2b-2.