Consider the smooth parametric curve 6 defined by the equations t (t²-3) { 3 (t²- 3)' = = where t€ R. 1. Show that the curve C has a horizontal tangent line at the point (0, –9). d²y 2. Evaluate the second derivative at the point (0, -9). dx²

Algebra and Trigonometry (MindTap Course List)
4th Edition
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Author:James Stewart, Lothar Redlin, Saleem Watson
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Chapter8: Polar Coordinates And Parametric Equations
Section8.CT: Chapter Test
Problem 8CT
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Consider the smooth parametric curve 6 defined by the equations
t (t²-3)
{
3 (t²- 3)'
=
=
where t€ R.
1. Show that the curve C has a horizontal tangent line at the point (0, –9).
d²y
2. Evaluate the second derivative at the point (0, -9).
dx²
Transcribed Image Text:Consider the smooth parametric curve 6 defined by the equations t (t²-3) { 3 (t²- 3)' = = where t€ R. 1. Show that the curve C has a horizontal tangent line at the point (0, –9). d²y 2. Evaluate the second derivative at the point (0, -9). dx²
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