Question

The point
P(7, −4)
lies on the curve
y = 4/(6 − x).
(a) If Q is the point
(x, 4/(6 − 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) 6.9
mPQ =


(ii) 6.99
mPQ =


(iii) 6.999
mPQ =


(iv) 6.9999
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).

Answer 1

well,
(a)(i)
4/(6-6.9) = 4/-.9 = -4.44
mPQ = (-4-(-4.444))/(7-6.9) = .444/.1 = 4.444

similarly for the other points

(b) I expect you will guess m=4
(c) now you have a point and a slope, so the line is

y+4 = 4(x-7)