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Let C be the curve with parametric equations

Let C be the curve with parametric equations

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.4: Plane Curves And Parametric Equations
Problem 20E
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1. Let C be the curve with parametric equations x= 3t - t² t-1 and y = ln(t-1) for t€ (1, +∞), and let P be the point (0, In 2). a. Find the value of t which corresponds to the point P. b. Without finding a Cartesian equation for the curve C, find an equation of the tangent line to Cat the point P. Leave your answer in point-slope form. c. Determine if C is concave up or down at P.
Transcribed Image Text:1. Let C be the curve with parametric equations x= 3t - t² t-1 and y = ln(t-1) for t€ (1, +∞), and let P be the point (0, In 2). a. Find the value of t which corresponds to the point P. b. Without finding a Cartesian equation for the curve C, find an equation of the tangent line to Cat the point P. Leave your answer in point-slope form. c. Determine if C is concave up or down at P.
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