The point P (9, 3) lies on the curve y = 3/(8 x ).

P

lies on the curve yx

(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).