Can Infinity be an absolute maximum?

If a limit is infinity or negative infinity, these cannot be considered as the absolute extrema values. 3. The greatest function value is the absolute maximum value and the least is the absolute minimum value.

Can there be no absolute maximum?

Since an absolute maximum must occur at a critical point or an endpoint, and x = 0 is the only such point, there cannot be an absolute maximum.

What counts as an absolute maximum?

An absolute maximum point is a point where the function obtains its greatest possible value. Similarly, an absolute minimum point is a point where the function obtains its least possible value.

Can a relative maximum be an absolute maximum?

1 Answer. A relative maximum or minimum occurs at turning points on the curve where as the absolute minimum and maximum are the appropriate values over the entire domain of the function. In other words the absolute minimum and maximum are bounded by the domain of the function.

Can there be an absolute maximum at a hole?

Absolute Maximum of f: the highest point that the graph of ƒ reaches in an interval. Holes cannot be maximums! Absolute Minimum of f: the lowest point that the graph of ƒ reaches in an interval. Holes cannot be minimums!

How To Count Past Infinity

Can an endpoint be a local maximum?

The answer at the back has the point (1,1), which is the endpoint. According to the definition given in the textbook, I would think endpoints cannot be local minimum or maximum given that they cannot be in an open interval containing themselves.

Is it possible that F X has no absolute maximum and minimum?

A function may have both an absolute maximum and an absolute minimum, have just one absolute extremum, or have no absolute maximum or absolute minimum. If a function has a local extremum, the point at which it occurs must be a critical point. However, a function need not have a local extremum at a critical point.

Can a cusp be an absolute minimum?

There could possibly be some x = b such that f(b) > f(a) on your interval in which case, your cusp is not a absolute/global maximum. 2. Depends. If the two relative minima are the absolute minima, then there you go, there's your absolute minima.

Can a relative minimum be a relative maximum?

A relative maximum or minimum is slightly different. All that's required for a point to be a relative maximum or minimum is for that point to be a maximum or minimum in some interval of x 's around x=c .

Can there be more than one global maximum?

Global refers to the entire domain of the function. Global extrema are also called absolute extrema. There can be only one global maximum value and only one global minimum value.

How do you know if a graph has an absolute maximum?

Absolute Maximum of a Graph: The absolute maximum of a given graph is the point on the entire graph with the highest y-value.

Can an endpoint be a relative max or min?

Relative extrema can certainly occur at endpoints of a domain. For instance, the function f(x) = x on the interval [0, 1] has a relative maximum at x = 1 and a relative minimum at x = 0.

Can a graph have more than one absolute maximum?

Important: Although a function can have only one absolute minimum value and only one absolute maximum value (in a specified closed interval), it can have more than one location (x values) or points (ordered pairs) where these values occur.

Can an endpoint be a critical point?

There is not much mathematical value in the question "can critical points occur at endpoints" because it is merely a matter of definition. Critical points are usually defined as points where the first derivative vanishes, so no end points can be critical points (as there is no derivative).

Can there be an absolute max on an open interval?

For the extreme value theorem to apply, the function must be continuous over a closed, bounded interval. If the interval I is open or the function has even one point of discontinuity, the function may not have an absolute maximum or absolute minimum over I.

Is a critical point always a maximum or minimum?

Determine whether each of these critical points is the location of a maximum, minimum, or point of inflection. For each value, test an x-value slightly smaller and slightly larger than that x-value. If both are smaller than f(x), then it is a maximum. If both are larger than f(x), then it is a minimum.

Can there be extrema on cusp?

The relative extrema of a function (if any) occur at critical points. But this does not mean that relative extrema occur at every critical point (they could be points of inflection, for example). Relative maximums and minimums may occur when the first derivative is not zero (like a cusp).

Can a function not have a global max or min?

Notice also that a function does not have to have any global or local maximum, or global or local minimum. Example: f(x)=3x + 4 f has no local or global max or min.

What conditions must be met to ensure that a function has an absolute maximum value and an absolute minimum value on an interval?

QUESTION: What conditions must be met to ensure that a function has an absolute maximum value and an absolute minimum value on an interval? ANS: The function must be a continuous function on a closed interval.

Can there be extrema on a discontinuous interval?

If the function is continuous and bounded and the interval is closed, then there must exist an absolute maximum and an absolute minimum. If a function is not continuous, then it may have absolute extrema at any points of discontinuity.

Can there be 2 global minimums?

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. The Global Maximum is about 3.7.

At which point does the graph have its maximum value?

The maximum value of a function is the place where a function reaches its highest point, or vertex, on a graph. If your quadratic equation has a negative a term, it will also have a maximum value.