Consider the parametric curve given by x (t) y(t) = t³ + 3t² = t² + t } 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.
Consider the parametric curve given by x (t) y(t) = t³ + 3t² = t² + t } 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.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Please answer parts iv, v and vi
![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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff167e2a2-2435-40d7-a5f0-abeb1524f8f0%2F9b0fb29d-9405-43f7-9adb-34e28187fc12%2Fz5l86e_processed.png&w=3840&q=75)
Transcribed Image Text: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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