The point p(7, −4) lies on the curve y = 4/(6 − x). (a) if q is the point (x, 4/(6 − 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. 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).