Question

True or False: The folowing function has no absolute maximum * (1 Point)​

Answer 1

Answer: True

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Explanation:

The absolute maximum is the largest y output of a function. Visually, it is always located at the highest point on the curve. It appears that y = 2 is the absolute maximum because of the highest point (3,2). However, this is an open hole which is not part of the graph. Think of the curve like a road, and the open hole is a pothole you can't drive over.  

Since (3,2) is not part of the graph, this means we can't reach y = 2 itself. We can get closer and closer to 2 from the underside, but that's about it. So this is why this graph does not have an absolute maximum. The absolute minimum doesn't exist either for similar reasoning.

Put another way, let's say we could claim there is an absolute max and the claim is that it's y = 1.999; the problem with this statement is that we can get closer to 2 by claiming the absolute max is y = 1.9999, and then we can get closer at y = 1.99999 and so on. We'll never be able to reach 2 itself.

Therefore, the claim "the function has no absolute maximum" is true.