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)