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Calculus 1 finding absolute max and min

  1. Oct 24, 2009 #1
    A University of Rochester student decided to depart from Earth after his graduation to find work on Mars. Before building a shuttle, he conducted careful calculations. A model for the velocity of the shuttle, from liftoff at t = 0 s until the solid rocket boosters were jettisoned at t = 79.2 s, is given by

    v(t)=0.001397167t3−0.080965t2+16.02t−039

    (in feet per second). Using this model, estimate
    the absolute maximum value
    and absolute minimum value (I found this through using Wolfram Alpha I don't understand how I get it though which is a problem)
    of the acceleration of the shuttle between liftoff and the jettisoning of the boosters.


    I got the derivative to be

    v'(t)= 0.004191201t2-0.16193t+16.02

    I imagine that I would have to find the critical points of this to get the max and min

    So I used the quadriatic formula but I am getting imaginary numbers when I do this so I am having trouble coming up with the absolute maximum and minimum any help would be appreciated.
     
  2. jcsd
  3. Oct 24, 2009 #2

    Mark44

    Staff: Mentor

    I assume you're looking for the absolute maximum value of the velocity.

    For v(t), why do you have 039 as the constant term? Is that 39 or is there a decimal point missing in it?

    Your v'(t) looks about right, and I find also that the solutions to v'(t) = 0 are complex, meaning that there are no real solutions to v'(t) = 0. This means that v'(t) > 0 for all t or that v'(t) < 0 for all t (not likely).

    Since there are no times for which v'(t) = 0, to find the maximum and minimum values of v(t), check the endpoints of your domain, which is implied in your problem description.
     
  4. Oct 24, 2009 #3
    it is supposed to be 0.39 instead of 39. I will try that what you suggest.
     
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