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lavenderish
 3 years ago
Can the endpoints of a function be a local/absolute maximum/minimum?
lavenderish
 3 years ago
Can the endpoints of a function be a local/absolute maximum/minimum?

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LogicalApple
 3 years ago
Best ResponseYou've already chosen the best response.2Consider 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.

LogicalApple
 3 years ago
Best ResponseYou've already chosen the best response.2After 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.
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