Chapter 4.8, Problem 47E

To determine

To sketch: a graph of the given function using graphing calculator, and to find the time during the stroke is the swimmer traveling the fastest.

Answer to Problem 47E

The swimmer is travelling fastest about 0.94 sec into the stroke.

Explanation of Solution

Given information:

The function,

  $S=-241t^7+1060t^6-1870t^5+1650t^4-737t^3+144t^2-2.43t.$

Models the speed $S$ of the swimmer during one complete stroke, where $t$ is the number of seconds since the start of the stroke and $0\le t\le 1.22$ .

Calculation:

Input function using key $-241X\wedge 7+1060X\wedge 6-1870X\wedge 5+1650X\wedge 4-737X\wedge 3+144X{x}^2-2.43X$ .

The display is shown below:

  

Adjust the WINDOW and hit GRAPH key.

  

Press 2^ndTRACE to go the CALCULATE menu and highlight the Maximum and press ENTER.

  

When asked for left bound and right bound, move cursor to the left or right of observed Maximum location.

When asked for Guess, simply Hit ENTER key.

  

Therefore, local maximum is at approximately $\left(0.94,3.63\right)$ .

Therefore, the swimmer is travelling fastest about 0.94 sec into the stroke.