Let be the quadratic function
- Find the slope of the chord joining the points on the graph of for and .
- Find (in terms of and ) the values of for which the tangent at has the same slope as the chord in part (a).
- The points on the graph of at and are and . So the chord joining them has slope given by the difference quotient (or “rise over run” if you like),
- The slope of the tangent line to the graph of is given by
Since we calculate the slope of the chord in part (a) as we set these equal and obtain,