Let P be the point with Cartesian coordinates (3, 7) and C be the curve on the Cartesian plane with parametric equations Sr = 2t2 + 1 ly = t5 + 5t3 +t² dy in terms of the parameter t without eliminating t. Simplify your answer. dx 1. Express 2. Find the value of t that corresponds to the point P which is on the curve C. 3. Using the result of items 1 and 2, determine the tollowing: (a) The equation of the tangent line to curve C at P, in point-slope form. (b) The concavity of C at P.

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 35E
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Only number 3.
I. Let P be the point with Cartesian coordinates (3, 7) and C be the curve on the Cartesian plane with
parametric equations
x = 2t? + 1
ly = t5 + 5t3 + t²
1. Express
dy
in terms of the parameter t without eliminating t. Simplify your answer.
d.x
2. Find the value of t that corresponds to the point P which is on the curve C.
3. Using the result of items 1 and 2, determine the tollowing:
(a) The equation of the tangent line to curve C at P, in point-slope form.
(b) The concavity of C at P.
Transcribed Image Text:I. Let P be the point with Cartesian coordinates (3, 7) and C be the curve on the Cartesian plane with parametric equations x = 2t? + 1 ly = t5 + 5t3 + t² 1. Express dy in terms of the parameter t without eliminating t. Simplify your answer. d.x 2. Find the value of t that corresponds to the point P which is on the curve C. 3. Using the result of items 1 and 2, determine the tollowing: (a) The equation of the tangent line to curve C at P, in point-slope form. (b) The concavity of C at P.
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