The point P(4, -2) lies on the curve y = 2/(3 – x). (a) If Q is the point (x, 2/(3 – x)), 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 mpo = (ii) 3.99 mp = (iii) 3.999 mPQ = (iv) 3.9999 mpQ = (v) 4.1 mPQ = (vi) 4.01 mpg = (vii) 4.001 mpQ = (viii) 4.0001 mpQ = (b) Using the results of part (a), guess the value of the slope m of the tangent line to the curve at P(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 91E
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find the slope mPQ of the secant line PQ (correct to six decimal places) for the following values of x.

The point P(4, -2) lies on the curve y = 2/(3 - x).
(a) If Q is the point (x, 2/(3 - x)), 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
mpQ =
(ii)
3.99
mpQ =
(iii)
3.999
mpo =
(iv) 3.9999
mpQ =
(v) 4.1
mpQ =
(vi) 4.01
mpQ =
(vii)
4.001
mpQ =
(viii)
4.0001
MPQ =
(b) Using the results of part (a), guess the value of the slope m of the tangent line to the curve at P(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/(3 - x)), 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 mpQ = (ii) 3.99 mpQ = (iii) 3.999 mpo = (iv) 3.9999 mpQ = (v) 4.1 mpQ = (vi) 4.01 mpQ = (vii) 4.001 mpQ = (viii) 4.0001 MPQ = (b) Using the results of part (a), guess the value of the slope m of the tangent line to the curve at P(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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