Find relative extrema f ( x ) = x2 on [-2, 2], Mathematics

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Recognizes the absolute extrema & relative extrema for the given function.

 f ( x ) = x2       on                  [-2, 2]

Solution

Following is the graph for this function.

1110_minimum1.png

In this case still we contain a relative & absolute minimum of zero at x = 0 .  Still we also have an absolute maximum of four. This will occur at two points, x = -2 and x = 2 .

Again, the function doesn't contain any relative maximums.

As this instance has illustrated there can only be a single absolute maximum or absolute minimum value, but they can occur at more than one place in the domain.


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