A University of Rochester student decided to depart from Earth after his graduation to find work...
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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 {eq}\displaystyle t=0 \ s {/eq} until the solid rocket boosters was jettisoned at {eq}\displaystyle t = 39.9 \ s {/eq}, is given by {eq}\displaystyle v(t) = 0.001573833t^3-0.081985t^2 + 18.95t + 2.82 {/eq} (in feet per second). Using this model, estimate the absolute maximum value and absolute minimum value of the acceleration of the shuttle between liftoff and the jettisoning of the boosters.
Absolute Extrema:
The graph of a function may or may not have absolute extrema if we examine its entire domain. However, if we look at only a closed interval, we will have both an absolute maximum and an absolute minimum as long as our function is continuous.
Answer and Explanation: 1
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View this answerFirst, notice that we want to find the absolute extrema of the acceleration, not of the velocity. This means that we first need to define the...
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Extreme Value Theorem | Proof & Examples
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Chapter 5 / Lesson 6
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In this lesson, discover what is the extreme value theorem. See the extreme value theorem proof. Learn about the Bolzano theorem. With the help of examples see the applications of the extreme value and Bolzano theorem.
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