Question

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

Answer 1

2

Explanation:

Slope equals `dy/dx = (dy"/"dt)/(dx"/"dt)`

`dy/dt = d/dt(2t) = 2`

`dx/dt = d/dt(t-2) = 1`

`therefore dy/dx = 2/1 = 2`

This means that no matter what `t` is, the slope of the curve at time `t` will always be 2.

So `dy/dx]_(t=1) = 2`