Please answer parts iv, v and vi, considering the attached answers for i, ii and iii. PART iThe y axis intersection is (0,0) and (0,2)Therefore x axis intersection is at (0,0).PART iiHence the critical point is at (2,4).PART iiiThe stationary point is a local maximum Consider the parametric curve given byx(t)t² + ty(t) = t³ + 3t²=}te [-π,5/4].(i) Find the axis intercepts.(ii) Find the critical points.(iii) Characterise the turning points.(iv) Find the extreme points.(v) Sketch the curve ensuring the direction of motion is indicated and all major points (from (i)–(iv))are labelled.(vi) Find the equation of the line tangent to the curve when t = 1.

The values of .The slope the tangent at is the derivative of the given curve at .The derivative of…

(iv) Find the extreme points. (v) Sketch the curve ensuring the direction of motion is indicated and all major points (from (i)–(iv)) are labelled. (vi) Find the equation of the line tangent to the curve when t = 1.

(iv) Find the extreme points. (v) Sketch the curve ensuring the direction of motion is indicated and all major points (from (i)–(iv)) are labelled. (vi) Find the equation of the line tangent to the curve when t = 1.

Trigonometry (MindTap Course List)

10th Edition

ISBN:9781337278461

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Topics In Analytic Geometry

Section6.6: Parametric Equations

Problem 5ECP: Write parametric equations for a cycloid traced by a point P on a circle of radius a as the circle...

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Question

Please answer parts iv, v and vi, considering the attached answers for i, ii and iii.

PART i
The y axis intersection is (0,0) and (0,2)
Therefore x axis intersection is at (0,0).
PART ii
Hence the critical point is at (2,4).
PART iii
The stationary point is a local maximum

Consider the parametric curve given by
x(t)
t² + t
y(t) = t³ + 3t²
=
}
te [-π,5/4].
(i) Find the axis intercepts.
(ii) Find the critical points.
(iii) Characterise the turning points.
(iv) Find the extreme points.
(v) Sketch the curve ensuring the direction of motion is indicated and all major points (from (i)–(iv))
are labelled.
(vi) Find the equation of the line tangent to the curve when t = 1.

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