I know the derivatives are and
how are the equations of 2 tangent lines found to both graphs
the answers are: and
2. Let P(p, p²) denote the tangent point on the parabola p and Q(q, -q²+6q-5) the tangent point on the parabola q.
3. The tangent to p at P has the equation:
and the tangent to q at Q has the equation
4. Both equations describe the same line. Thus
5. Solve this system of simultaneous equations for p and q. Resubstitute the result into the equations of and .
6. For confirmation: Draw the 2 parabolas and the tangents.
I suspect that the problem is asking for lines that at tangent to both of these graphs. Suppose y= mx+ b is the equation of such a tangent line. At the point, where that line is tangent to we must have and . At the point, where it is tangent to , we must have and so we have 4 equations to solve for m, b, , and