Question

Find the rate of change of f, df/dt, along the parametric curve x(t)=2t-1, y(t)=3-2t^2 at t=1.

Answer 1

We have \(f(t)=(2t−1,3−2t^2)\) then \(Df(t)=(Df_1(t),Df_2(t))=(2,−4t)\)
So now we evaluate it at \(t=1\) and we have
$$Df(1)=(2,−4(1))=(2,−4)$$

Answer 2

But the answer should be -8.

Answer 3

Are they asking for the slope of the tangent at \(t=1\)?