The figure shows the curve together with the line which has slope and passes through point .
Write a cubic polynomial whose roots are the numbers , , and 1.
Divide this polynomial by to get a quadratic that is a multiple of .
Since , determine in terms of .
Imagine changing the value of the slope so that the value of gets closer and closer to 1. When , the line will be tangent to the curve at the point . Determine the equation of the tangent to the curve at the point .