7F - Absolute maximums and minimums
While many problems will be solved by finding maximum or minimum values associated with stationary points it is always important to test the endpoints of a practical domain as they may represent absolute maximum or absolute minimum values not found using calculus. These are also known as global maximum or global minimum values.
- On CAS you can use fMin and fMax commands to find absolute minimum or maximum values.
- By-hand, you can find the values of the endpoint(s) by substituting the \(x\)-values of any endpoints into the function.
7F - Example 1: Absolute maxima and absolute minima (CAS)
A modified version of the surf lifesaving Ironman consists of three events. A competitor runs along a straight beach from point \(F\) to point \(A\), the competitor then swims around a buoy at point \(B\) then back to point \(F\). The competitor then runs along the straight beach to the point \(D\) where they collect a board and paddle around a buoy at point \(E\) an then finish the race when they arrive back at point \(F\). A diagram of the race is shown below.
The point \(F\) can be moved anywhere between points \(A\) and \(D\). Let \(x\) be the distance, in metres, between points \(A\) and \(F\).
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7F - Example 1: Video solution
7F - Example 1: Practice
Question 1: ABC Question 2: ABC 7F - Example 1: Solutions
Question 1: ABC Question 2: ABC |