The point P(9, −3) lies on the curve y = 3/(8−x). (a) If Q is the point (x, 3/(8−x)), use your calculator to find the slope mPQ of the secant line PQ (correct to six decimal places) for the following values of x. (i) 8.9 mPQ = (ii) 8.99 mPQ = (iii) 8.999 mPQ = (iv) 8.9999 mPQ = (v) 9.1 mPQ = (vi) 9.01 mPQ = (vii) 9.001 mPQ = (viii) 9.0001 mPQ = (b) Using the results of part (a), guess the value of the slope m of the tangent line to the curve at P(9, −3). m = (c) Using the slope from part (b), find an equation of the tangent line to the curve at P(9, −3).
