I've got a question， it's about how we modify an equation so that the t inside it could take both positive and negative values
So this is my curvature κ(t): (2t^(3)/(4+t^(4))^(3/2）I've attached the result done by WolframAlpha below and I've done it by myself in order to make sure that there's no computation error. I've inputted the result directly, but the system don't accept it
Somehow, the system still does not accept my answer and I've asked my instructor regarding this problem. He said that by definition, the curvature of a curve is positive, so the parameter t in the question must be capable of taking both positive and negative values. So if we put a negative number into the t of the equation I mentioned, the result would be negative. I'm really running out of ideas. Does anyone know how to modify this equation? Any tips or ideas would be very appreciated, Please give me an enlightenment. Thank you very much.
(Please don't judge me based on my stupidity, I'm an engineering student and I know this is kinda stupid question. My math isn't too good, but I'm really trying, please understand :( ）
To make the question answered.
You calculations are almost correct (except $4^3$ instead of $2^3$ near the end), but when you calculated $|r’(t)\times r’’(t)|$ you forgot to take the absolute value, and the correct value should be $16|t|^{-3}$.