10.9#4

I have attempted to solve this problem many times by 1) finding the velocity vector 2) finding the magnitude of the velocity vector (speed) 3) taking the derivative of the velocity vector and equaling it to zero 4) solving for t. I have gotten 3/52 seconds every time, but I am incorrect. What am I doing wrong? My original position vector is: <-5t^2,-2t,t^2-6t>



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So first a meta-analysis. solving a problem incorrectly many times is frustrating, but it's also a sign post that you missed: when you solve something incorrectly its important to figure out what you don't understand that caused your mistake. Just doing it over again usually won't help.

Secondly, you haven't told me enough of what you did that I can tell you exactly what you did wrong, but I can see that you're off by a factor of 2. Maybe this is because you're getting tangled up in the square root or maybe you incorrectly used FOIL when you multiplied out d/dt (t^2-6t). 

I guess you correctly computed that r'(t) = <-10t, -2, 2t - 6 >, did you get 
s(t) = √(100t^2 + 4 + (2t-6)^2) = √(104t^2 - 24t + 40)?

At this point you could use the chain rule, or you could recognize that s(t) and s(t)^2 are minimum at the same time; the latter is a little tidier to minimize because it's a polynomial.















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