Can a relative maximum be an absolute maximum?

However, unlike the first example this will occur at two points, x=−2 x = − 2 and x=2 x = 2 . Again, the function doesn’t have any relative maximums. 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.

Can a relative maximum be the same as an absolute maximum?

Therefore, an absolute maximum is always a relative maximum. If a function has an absolute maximum, it has a relative maximum.

Is local maximum absolute maximum?

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.

What is relative maximum and relative minimum?

A relative maximum point is a point where the function changes direction from increasing to decreasing (making that point a “peak” in the graph). Similarly, a relative minimum point is a point where the function changes direction from decreasing to increasing (making that point a “bottom” in the graph).

Can the absolute max be infinity?

If a limit is infinity or negative infinity, these cannot be considered as the absolute extrema values.

Can absolute maximum be an open circle?

Note, the open circles on the graph mean that those points are missing, so there cannot be any extrema at those points. This graph is defined on the open interval, (-4, 4). There are no absolute extrema.

Can you have an absolute minimum at an endpoint?

Notice that the absolute minimum value is obtained within the interval and the absolute maximum value is obtained on an endpoint.