A particle moves along the x-axis so that its position at any time t 0 is given by x(t) = t^4 - 10t^3 + 29t^2 - 36t +2. For which value of t is the speed the greatest?

Question

A particle moves along the x-axis so that its position at any time t> 0 is given by x(t) = t^4 - 10t^3 + 29t^2 - 36t +2. For which value of t is the speed the greatest?

experimentx · Answer

find maxima

anonymous · Answer

Maximum at first derivative or second?

experimentx · Answer

o.. sorry, take derivative ... the resulting function will give you speed.

experimentx · Answer

and the usual process of maxima

anonymous · Answer

|dw:1334044638555:dw| The derivative graph looks something like this... where is the maximum?

experimentx · Answer

do we have any interval of time given??

anonymous · Answer

No, t>0

experimentx · Answer

it seems that we have local maximum but's that negative ... I guess at infinity then.

anonymous · Answer

Lol, but it's multiple choice..
A. t= 1
B. t= 2
C. t= 3
D. t= 4
E. t=5

experimentx · Answer

the distance is actually decreasing.

experimentx · Answer

http://www.wolframalpha.com/input/?i=x%28t%29+%3D+t%5E4+-+10t%5E3+%2B+29t%5E2+-+36t+%2B2

experimentx · Answer

http://www.wolframalpha.com/input/?i=maxima+f%28t%29+%3D+4t%5E3+-+30t%5E2+%2B+58t+-+36

anonymous · Answer

What does that mean for speed? Sorry, I do not understand..

experimentx · Answer

http://www.wolframalpha.com/input/?i=maxima+d%28t%5E4+-+10t%5E3+%2B+29t%5E2+-+36t+%2B2%29%2Fdt

experimentx · Answer

speed is rate of change of distance ... should always be positive.

anonymous · Answer

Oh, ok thanks.