The point P(7, −4) lies on the curve y = 4/(6 − x). (a) If Q is the point (x, 4/(6 − 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) 6.9 mPQ = (ii) 6.99 mPQ = (iii) 6.999 mPQ = (iv) 6.9999 mPQ = (v) 7.1 mPQ = (vi) 7.01 mPQ = (vii) 7.001 mPQ = (viii) 7.0001 mPQ = (b) Using the results of part (a), guess the value of the slope m of the tangent line to the curve at
P(7, −4). m = (c) Using the slope from part (b), find an equation of the tangent line to the curve at
P(7, −4).