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lavenderish Group Title Can the endpoints of a function be a local/absolute maximum/minimum? one year ago one year ago

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1. LogicalApple

Consider the function $f(x) = \sqrt{x}$ Or an arbitrary function of your choice. Any point can be a local min or max, or a global min or max.

2. LogicalApple

After some research I will retract what I said. Endpoints can be global but not local because of the way local extrema is defined. There would have to be a neighborhood around a point in order for it to be considered a local minimum or maximum. So end points can be global extrema but not local ones.