Avoid non-standard compiler extensions and implement it as a completely type-safe macro in pure standard C ISO This control macro, if implemented for the given type, is used to check that both parameters are of the correct type. If the type is not supported, there will be a compiler error. More such macros can be added if more types are supported.
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Minimum and Maximum Values Many of our applications in this chapter will revolve around minimum and maximum values of a function. While we can all visualize the minimum and maximum values of a function we want to be a little more specific in our work here. In particular, we want to differentiate between two types of minimum or maximum values.
Also, we will collectively call the minimum and maximum points of a function the extrema of the function. So, relative extrema will refer to the relative minimums and maximums while absolute extrema refer to the absolute minimums and maximums. A relative maximum or minimum is slightly different.
This means that relative extrema do not occur at the end points of a domain.
They can only occur interior to the domain. There is actually some debate on the preceding point. Some folks do feel that relative extrema can occur on the end points of a domain. This will be discussed in a little more detail at the end of the section once we have a relevant fact taken care of.
Both of these points are relative maximums since they are interior to the domain shown and are the largest point on the graph in some interval around the point.
These two points are the largest and smallest that the function will ever be. We can also notice that the absolute extrema for a function will occur at either the endpoints of the domain or at relative extrema. Example 1 Identify the absolute extrema and relative extrema for the following function.
Here is the graph, Note that we used dots at the end of the graph to remind us that the graph ends at these points. We can now identify the extrema from the graph. As we saw in the previous example functions do not have to have relative extrema. Example 2 Identify the absolute extrema and relative extrema for the following function.
We also still have an absolute maximum of four. As this example has shown there can only be a single absolute maximum or absolute minimum value, but they can occur at more than one place in the domain. Example 3 Identify the absolute extrema and relative extrema for the following function.
For this function that means all the real numbers. Here is the graph. So, some graphs can have minimums but not maximums. Likewise, a graph could have maximums but not minimums.
Example 4 Identify the absolute extrema and relative extrema for the following function. This function has no relative extrema. Example 5 Identify the absolute extrema and relative extrema for the following function.
In this case the function has no relative extrema and no absolute extrema.Get the free "Max/Min Finder" widget for your website, blog, Wordpress, Blogger, or iGoogle. Find more Mathematics widgets in Wolfram|Alpha.
To see the MIN and MAX formulas, you can download the MIN and MAX sample file. The file is in Excel / formatt, and zipped. The file is in Excel / formatt, and zipped.
For more information on array formulas, I recommend Mike Girvin's book, Ctrl+Shift+Enter: Mastering Excel Array Formulas. Get the free "Max/Min Finder" widget for your website, blog, Wordpress, Blogger, or iGoogle. Find more Mathematics widgets in Wolfram|Alpha.
Max and Min's. Can you find the local maximum and local minimum in the graph above? Yes, of course. Now look at the same places and think about what the slope is at those two locations.
Correct, the slope is zero at those locations.
Is the slope equal to zero anywhere else on the graph? The answer is . The maximum or minimum over the entire function is called an "Absolute" or "Global" maximum or minimum. There is only one global maximum (and one global minimum) but there can be more than one local maximum or minimum.
Where are MIN and MAX defined in C, if at all?. They aren't. What is the best way to implement these, as generically and type safe as possible (compiler extensions/builtins for mainstream compilers preferred).