The point P(2, −1) lies on the curve y = 1/(1 − x). a. If Q is the point (x, 1/(1 − x)), use your calculator to find the slope of the secant line PQ (correct to six decimal places) for the following values of x:

1. 1.5
2. 1.9
3. 1.99
4. 1.999
5. 2.5
6. 2.1

b. Using the results of part (a), guess the value of the slope of the tangent line to the curve at P(2,-1).
c. Using the slope from part (b), find an equation of the tangent line to the curve at P(2,-1).