Question

What is the slope of `f(t) = (-4t^2+2t,2t)` at `t =-1`?

Answer 1

`1/5`

Explanation:

`x'(t)=-8t+2`
`y'(t)=2`

The derivative of the parametric function is

`dy/dx=(y'(t))/(x'(t))=2/(2-8t)=1/(1-4t)`

To find the slope when `t=-1`, plug that value into the `dy/dx` expression.

`1/(1-4(-1))=1/(1+4)=1/5`