The point P (9, ?4) lies on the curve y = 4/(8 ? x ). (a) If Q is the point ( x

Question

The point

P(9, ?4)

lies on the curve

y = 4/(8 ? x).

(a) If Q is the point

(x, 4/(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, ?4).

m =

(c) Using the slope from part (b), find an equation of the tangent line to the curve at

P(9, ?4).

Explanation / Answer

df(x)/dx=   4/(8?x)2

(i). mPQ = 4.938

(ii). mPQ = 4.081

(iii). mPQ = 4.008

(iv). mPQ = 4.000

(v). mPQ = 3.306

(vi). mPQ = 3.921

(vii). mPQ = 3.992

(viii). mPQ = 3.999

(b). slope m =4

(c). y= 4x -40

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