Find the points on the curve

label Calculus
account_circle Unassigned
schedule 1 Day
account_balance_wallet $5

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

Did you know? You can earn $20 for every friend you invite to Studypool!
Click here to
Refer a Friend
...
Apr 3rd, 2015
...
Apr 3rd, 2015
Jun 27th, 2017
check_circle
Mark as Final Answer
check_circle
Unmark as Final Answer
check_circle
Final Answer

Secure Information

Content will be erased after question is completed.

check_circle
Final Answer