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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 mpQ = (ii) 3.99 mpQ = (iii) 3.999 mpQ = (iv) 3.9999 mpq = 4.1 mpQ = (vi) 4.01 mpQ = (viii) (vii) 4.001 mpQ = mpQ = 4.0001 (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).

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 mpQ = (ii) 3.99 mpQ = (iii) 3.999 mpQ = (iv) 3.9999 mpq = 4.1 mpQ = (vi) 4.01 mpQ = (viii) (vii) 4.001 mpQ = mpQ = 4.0001 (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
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 94E
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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 mpQ = (ii) 3.99 mpQ = (iii) 3.999 mpQ (iv) 3.9999 mpq = E = 4.1 mpQ = (vi) 4.01 mpQ = (viii) (vii) 4.001 mpQ = mpQ = 4.0001 (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 mpQ = (ii) 3.99 mpQ = (iii) 3.999 mpQ (iv) 3.9999 mpq = E = 4.1 mpQ = (vi) 4.01 mpQ = (viii) (vii) 4.001 mpQ = mpQ = 4.0001 (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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