I have found the equation for unit vector:

T(t) = <2t, 2t^2, 1> / sqrt(4t^2 + 4t^4 + 1)

and it has been verified as correct. I now have to calculate N(t) which I know to be T'(t) / magnitude (T'(t)) at t = -3

so to find a general form for N(t) I did the quotient rule to find T'(t), then plugged in my -3 and I am just getting ridiculous numbers and it's not working out at all.

I have:

T'(t) = (4t^2+4t^4+1)^.5 <2, 4t, 0> -
<2t, 2t^2, 1>[.5(4t^2 + 4t^4+1)^-.5)
all over (4t^2 + 4t^4 + 1)

plugging in t = -3

19 < 2, -12, 0 > - < -6, 18, 1> (.5)(1/19)
361

Simplifying this all gives me horrible numbers...can anyone spot what I'm doing wrong or maybe I'm just messing all the algebra up?

Thanks in advance, I know this is a tedious problem, so I really appreciate the help!

-Jeff