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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.
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.
Extrema : Note as well that while we say an "open interval around x = c " we mean that we can discover some interval ( a, b ) , not involving the endpoints, such that a Also,
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