Chapter 1.4, Problem 3E

The point P $(2,-1)$ lies on the curve $y=1/\left(1-x\right)$.

(a) If Q is the point $(x,1/\left(1-4\right)$, use your calculator to find the slope of the secant line PQ (correct to six decimal places) for the following values of x:

(i) 1.5

(ii) 1.9

(iii) 1.99

(iv) 1.999

(v) 2.5

(vi) 2.1

(vii) 2.01

(viii) 2.001

(b) Using the results of part (a), guess the value of the slope of the tangent line to the curve at $P\left(2,-1\right)$.

(c) Using the slope from part (b), find an equation of the tangent line to the curve at $P\left(2,-1\right)$.