Posted by
**Nyk** on
.

The point P(8, −3) lies on the curve

y = 3/(7 − x).

(a) If Q is the point x, 3/(7 − 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) 7.9

mPQ =

(ii) 7.99

mPQ =

(iii) 7.999

mPQ =

(iv) 7.9999

mPQ =

(v) 8.1

mPQ =

(vi) 8.01

mPQ =

(vii) 8.001

mPQ =

(viii) 8.0001

mPQ =

(b) Using the results of part (a), guess the value of the slope m of the tangent line to the curve at

P(8, −3).

m =

(c) Using the slope from part (b), find an equation of the tangent line to the curve at P(8, −3).