Question

We have a parametric curve x = - 6t + t^3 + 1, y = -2t − t^2

a) Sketch a graph of the curve (use technology to help)

b) Find the equation of the tangent line at t = –1

c) Find the value(s) of t where the tangent is horizontal.

d) Find the value(s) of t where the tangent is vertical.

Answer 1

We are given parametric equations as

(a)

(b)

we can find derivatives

now, we can find dy/dx

now, we can plug t=-1

now, we can find points

now, we can use point slope form of line

............Answer

(c)

we can set top =0

and then we can solve for t

............Answer

(d)

we can set bottom =0

and then we can solve for t

and we get

............Answer