AP Calculus BC Parametrics

For what value(s) of t does the curve given by x = t³-t²-1 and y = t⁴+2t²-8t have a vertical tangent? 

• 0
• 1
• 0,2/3
• 0,2/3,1

 For the cardioid r = 1 + sinϴ, find the slope of the tangent when ϴ = π/3

• -π
• π
• -1
• 1

A curve in the plane is defined parametrically by the equations x = t³+t and y = t⁴+2t².  An equation of the line tangent to the curve at t = 1 is

• y=2x-1
• y=2x
• y=4x-5
• y=
  y=½x+5

If a particle moves in the xy-plan so that at time t > 0 its position vector is <ln(t²+2t), 2t²>, then at time t = 2, its velocity vector is

• <⅛,8>
• <¾,8>
• <¾,4>
• <-¾,8>

A particle moves in the xy plane with position given by (x(t), y(t)) = ( 5 - 2t , t²-3) at time t.  In which direction is the particle moving as it passes through the point (3, -2)? 

• To the right and down
• To the left and up
• To the left and down
• Straight left

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6