The point P(6, –4) lies on the curve y = 4/(5 – x). (a) If Q is the point (x, 4/(5 – x)), use your calculator to find the slope mPO of the secant line PQ (correct to six decimal places) for the following values of x. (i) 5.9 mpQ = (ii) 5.99 mpQ = (iii) 5.999 mpQ = (iv) 5.9999 mpQ = (v) 6.1 mpQ = (vi) 6.01 mPQ = (vii) 6.001 mpQ = (viii) 6.0001 mPQ = (b) Using the results of part (a), guess the value of the slope m of the tangent line to the curve at P(6, –4). m = (c) Using the slope from part (b), find an equation of the tangent line to the curve at P(6, -4).

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