Question

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

Answer 1

Slope at `t=1` is`1/4`.

Explanation:

The slope of a parametric function `f(t)=(x(t),y(t))` is given by `((dy)/(dt))/((dx)/(dt))`.

Here we have `x(t)=t^2+2t` and `y(t)=t-3`,

therefore `(dx)/(dt)=2t+2` and `(dy)/(dt)=1`

hence slope is `((dy)/(dt))/((dx)/(dt))=1/(2t+2)`

and at `t=1`, slope is `1/(2xx1+2)=1/4`