Calculus 1 finding absolute max and min

[Wm_Davies]

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.

 

[Mark44]

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.

 

[Wm_Davies]

it is supposed to be 0.39 instead of 39. I will try that what you suggest.