The point P(3, −3) lies on the curve y = 3/(2 − x). (a) If Q is the point (x, 3/(2 − 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. (b) Using the results of part (a), guess the value of the slope m of the tangent line to the curve at P(3, −3). (c) Using the slope from part (b), find an equation of the tangent line to the curve at P(3, −3).

The point P(3, −3) lies on the curve y = 3/(2 − x). (a) If Q is the point (x, 3/(2 − 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. (b) Using the results of part (a), guess the value of the slope m of the tangent line to the curve at P(3, −3). (c) Using the slope from part (b), find an equation of the tangent line to the curve at P(3, −3).

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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Question

The point P(3, −3) lies on the curve y = 3/(2 − x).

(a) If Q is the point (x, 3/(2 − x)), use your calculator to find the slope m_PQof the secant line PQ (correct to six decimal places) for the following values of x.

(b) Using the results of part (a), guess the value of the slope m of the tangent line to the curve at P(3, −3).

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