The point P(4,-2) lies on the curve y = 2/(3 - x). (a) If Q is the point (x, 2/(3x)), use your calculator to find the slope mpo of the secant line PQ (correct to six decimal places) for the following values of x. (i) 3.9 = 2.222222 mpQ= (ii) 3.99 mPQ =2.020202 (iii) 3.999 mpQ =2.002002 (iv) 3.9999 mpQ= =2.000200 (v) 4.1 тро= =1.818181 (vi) 4.01 mpQ= = 1.980980 (vii) 4.001 MPQ=1.998002 (viii) 4.0001 mpQ =1.999800 Enter a number. ۵ (b) Using the results of part (a), guess the value of the slope m of the tangent line to the curve at P(4,-2). M= (c) Using the slope from part (b), find an equation of the tangent line to the curve at P(4, -2).

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 94E
Question
The point P(4,-2) lies on the curve y = 2/(3 - x).
(a) If Q is the point (x, 2/(3x)), use your calculator to find the slope mpo of the secant line PQ (correct to six decimal places) for the following values of x.
(i) 3.9
= 2.222222
mpQ=
(ii)
3.99
mPQ
=2.020202
(iii) 3.999
mpQ
=2.002002
(iv)
3.9999
mpQ=
=2.000200
(v) 4.1
тро=
=1.818181
(vi) 4.01
mpQ=
= 1.980980
(vii) 4.001
MPQ=1.998002
(viii)
4.0001
mpQ
=1.999800
Enter a number.
۵
(b) Using the results of part (a), guess the value of the slope m of the tangent line to the curve at P(4,-2).
M=
(c) Using the slope from part (b), find an equation of the tangent line to the curve at P(4, -2).
Transcribed Image Text:The point P(4,-2) lies on the curve y = 2/(3 - x). (a) If Q is the point (x, 2/(3x)), use your calculator to find the slope mpo of the secant line PQ (correct to six decimal places) for the following values of x. (i) 3.9 = 2.222222 mpQ= (ii) 3.99 mPQ =2.020202 (iii) 3.999 mpQ =2.002002 (iv) 3.9999 mpQ= =2.000200 (v) 4.1 тро= =1.818181 (vi) 4.01 mpQ= = 1.980980 (vii) 4.001 MPQ=1.998002 (viii) 4.0001 mpQ =1.999800 Enter a number. ۵ (b) Using the results of part (a), guess the value of the slope m of the tangent line to the curve at P(4,-2). M= (c) Using the slope from part (b), find an equation of the tangent line to the curve at P(4, -2).
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