anonymous
  • anonymous
Hey :) Could you please with this Calculus, word problem? Two ants named Fred and Velma are walking backwards and forwards along a straight ruler marked in inches. Fred's distance from his starting point is F(t)= 4t - t^3 inches after t minutes have passed. Velma's distance from Fred's starting point is V(t)= (t^2) -12t +36 inches after t minutes have passed. Find the minimum distance between the two ants. Make sure to justify that this is a minimum. Please show how you solve this in detail. Thanks in advance
Mathematics
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
complicated... ill try and help
dumbcow
  • dumbcow
distance between 2 ants is V(t) - F(t) , when t>0 V(t) > F(t) now just differentiate V(t) - F(t) and set equal to 0 \[V'(t) - F'(t) = 0\] \[V'(t) = F'(t)\] \[2t-12 = 4-3t^{2}\] solve for t, you may get 2 solutions plug them in to verify which gives the minimum
dumbcow
  • dumbcow
@Eugenier2013 , does it make sense? did you get solution

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anonymous
  • anonymous
Thanks dumbcow for your help. Should I plug the solutions I get when I solve for t in V(t) or F(t) ?
dumbcow
  • dumbcow
you should plug them into " V(t) - F(t)" since that represents distance between ants

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