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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

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.5: Polar Coordinates
Problem 98E
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Please answer 1(a-e) thanks!
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 $3=(1)x ) hommen al evo norl syad) of bull magnet adr ovei ovurd of enllagrost odl qu ovsomo) 0 VND 5 to yd novig zi vomit te ploiting ooo to notizo 3200 S = C 2. Repeat the problem about the collision points discussed in recitation but this time describe what happens it the second particle is given instead by nia. x₂ = 3 + costru wol y₂ = 1 + sin tuolo 0≤t≤ 2π oy) esloineq diod to a 11 Tomilomes aft is only one sa ove stoine di o.o.I fainioq notillos noitesersta
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 $3=(1)x ) hommen al evo norl syad) of bull magnet adr ovei ovurd of enllagrost odl qu ovsomo) 0 VND 5 to yd novig zi vomit te ploiting ooo to notizo 3200 S = C 2. Repeat the problem about the collision points discussed in recitation but this time describe what happens it the second particle is given instead by nia. x₂ = 3 + costru wol y₂ = 1 + sin tuolo 0≤t≤ 2π oy) esloineq diod to a 11 Tomilomes aft is only one sa ove stoine di o.o.I fainioq notillos noitesersta
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