The point P(9, −2) lies on the curve y = 2 8 − x . (a) If Q is the point x, 2 8 − x , find the slope 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 of the tangent line to the curve at
P(9, −2).
m =
(c)
Using the slope from part (b), find an equation of the tangent line to the curve at
P(9, −2).