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

Question

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

anonymous · Answer

complicated... ill try and help

dumbcow · Answer

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 · Answer

@Eugenier2013 , does it make sense?
did you get solution

anonymous · Answer

Thanks dumbcow for your help. Should I plug the solutions I get when I solve for t in V(t) or F(t) ?

dumbcow · Answer

you should plug them into " V(t) - F(t)" since that represents distance between ants