I like to draw a picture to help me see what is going on.

So you know the derivative is

So the slope at the point is

So the equation of the tangent line is

but we know that the tangent line intersects the curse again at some point

So we know that

and that

So setting the two above equations equal gives

This is cubic in b which can make it difficult to solve but know that this is trivially true when so must be a factor of the equation by long division we get

this can be factored to gives

so the only non trivial root is

Now just plug the points into the derivative to get