Suppose f(.) is a continuous function over a closed and bounded interval [a, b]. Then there exists a point d in [a, b] where f(.) has a minimum, and a point c in [a, b] where f(.) has a maximum, so that f(d) <= f(x) <= f(c) for all x in [a, b]. The statement is derived from:
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Single-variable optimisation has come up 37 times in 6 exams since 2010.
This question is on Optimisation on a closed interval, part of Single-variable optimisation in Mathematics.
Global maxima and minima when the domain is bounded, including endpoints and existence.
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Question from the UGC-NET 2023 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.