4.2 Maximum and Minimum Values

Mathematica script by Chris Parrish,
cparrish@sewanee.edu

Problems from James Stewart,
"Calculus: Concepts and Contexts,"
Second Edition, Brooks/Cole, 2001

Space Shuttle Endeavour

Stewart, Exercise 4.2.54

We are keeping track of the timing of certain specific events that occur during the first 125 seconds of a launch of the Space Shuttle Endeavour.
The table shown below records the timing of those events, and the corresponding velocities of the Space Shuttle Endeavour for a specific launch.
See Stewart, Exercise 4.2.54, for details.

In[27]:=

Out[32]//TableForm=

 t (sec) 0 10 15 20 32 59 62 125 velocity (ft/sec) 0 185 319 447 742 1325 1445 4151

Let's plot those points.

In[33]:=

Now construct a cubic polynomial to approximate that data ...

In[35]:=

Out[35]=

In[36]:=

... and graph the polynomial and the data to verify that we have a reasonable correspondence.

In[38]:=

Now let's use the approximating poynomial to find a model for the acceleration of the shuttle.

In[39]:=

Use this picture to estimate the maximum and minimum values of the acceleration during the first 125 seconds of the launch.

Created by Mathematica  (March 16, 2004)