The point
p(6, −2)
lies on the curve
y = 2/(5 − x).
(a) if q is the point
(x, 2/(5 −
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) 5.9
mpq =
(ii) 5.99
mpq =
(iii) 5.999
mpq =
(iv) 5.
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, −2).
m =
(c) using the slope from part (b), find an equation of the tangent line to the curve at
p(6, −2).