Consider the parametric curve given by (a) Find dy/dx and d²y/dx² in terms of t. dy/dx = |d²y/dx² = x = t³ - 12t, y = 2t² - 2

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 34E
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Consider the parametric curve given by
(a) Find dy/dx and d²y/dx² in terms of t.
dy/dx =
d²y/dx² =
t-interval:
x =
< t <
t³ - 12t,
(b) Using "less than" and "greater than" notation, list the t-interval where the curve is concave upward.
Use upper-case "INF" for positive infinity and upper-case "NINF" for negative infinity. If the curve is never concave upward, type an
upper-case "N" in the answer field.
y = 2t² - 2
Transcribed Image Text:Consider the parametric curve given by (a) Find dy/dx and d²y/dx² in terms of t. dy/dx = d²y/dx² = t-interval: x = < t < t³ - 12t, (b) Using "less than" and "greater than" notation, list the t-interval where the curve is concave upward. Use upper-case "INF" for positive infinity and upper-case "NINF" for negative infinity. If the curve is never concave upward, type an upper-case "N" in the answer field. y = 2t² - 2
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