Let and be the polynomials:
Find values of such that and intersect at the point and have the same tangent line at this point.
Since we want and to intersect at the point we must have . This gives us the equations,
Next, we compute the derivatives so that we can find the slope of the tangent lines at this point,
Since these must be the same at the point we have
Then from above we know ; thus, .
Therefore, the values of the constants are