1. Consider the curve in parametric form x(t) = t³ - 3t a) Find the point(s) where the tangent line to the curve is horizontal y(t) = 3t²-9 b) Find the point(s) where the tangent line to the curve is vertical c) Find the points where there are more than one tangent line and find the equations of those lines d) Determine the values of t for which the curve in concave up or concave down e) Sketch the graph of the curve on the x-y-plane
1. Consider the curve in parametric form x(t) = t³ - 3t a) Find the point(s) where the tangent line to the curve is horizontal y(t) = 3t²-9 b) Find the point(s) where the tangent line to the curve is vertical c) Find the points where there are more than one tangent line and find the equations of those lines d) Determine the values of t for which the curve in concave up or concave down e) Sketch the graph of the curve on the x-y-plane
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 1(a-e) thanks!
Transcribed Image Text:ho12232
1. Consider the curve in parametric form x(t) = t³ - 3t
a) Find the point(s) where the tangent line to the curve is horizontal
y(t) = 3t² - 9
b) Find the point(s) where the tangent line to the curve is vertical
c) Find the points where there are more than one tangent line and find the equations of those lines
d) Determine the values of t for which the curve in concave up or concave down
e) Sketch the graph of the curve on the x- y- plane
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