Question

What is the slope of `f(t) = ((t-2)^3,2t)` at `t =-1`?

Answer 1

Slope at `t=-1` is `-1/3`

Explanation:

At `t=-1`, `f(t)=((-1-2)^2,2(-1))` or `f(t)=(9,-2)`

As `x=(t-2)^2`, `(dx)/(dt)=2(t-2)=2t-4`

and `y=2t`, `(dy)/(dt)=2`

Hence slope is `(dy)/(dx)=((dy)/(dt))/((dx)/(dt))=2/(2t-4)`

or `(dy)/(dx)=2/(2(-1)-4)=2/(-6)=-1/3`