Find the points on the curve

label Calculus
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Find the points on the curve where the tangent is horizontal or vertical. If you have a graphing device, graph the curve to check your work. 

x= t^3-3t

y = t^2-6

Horizontal curve? 

Vertical curve? 

Apr 3rd, 2015

dx/dt = 3t^2 -3

dy/dt= 2t

By the chain rule, you get dy/dx = 2t/ (3t^2-3).


Horizontal tangent lines happen when dy/dx= 0, so when 2t=0, so t=0. plugging t= 0 back to the x and y equations, x=0, y= -6, so (0, -6)

Vertical tangent lines happen when dy/dx is undefined, so when 3t^2-3, so when t= -1 and when t=1. plugging back to get x and y, we get (2,-5) and (-2, -5)


Apr 3rd, 2015

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Apr 3rd, 2015
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Apr 3rd, 2015
Oct 17th, 2017
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