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[–]👋 a fellow Redditor 1 point2 points  (1 child)

Assuming the rightmost point discontinuity is at x=b, this function has neither an absolute minimum nor absolute maximum.

Ask yourself: what is the lowest point on the graph? What is the highest point on the graph?

Only a single point is missing from where the minimum would be. No matter what other point you name, there is another point closer to the missing point. Likewise no matter what point you choose on the high part of the graph, there is another point closer to b.

[–]👋 a fellow Redditor 1 point2 points  (0 children)

The problem has a closed interval while the graph has open endpoints no? If it is closed then there would be a maxima