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Math Help - Calculus, Local and global extrema

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    Calculus, Local and global extrema

    Is it possible for a local minimum to be a global maximum? Similarly, is it possible for a local maximum to be a global minimum?
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    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by casemeister View Post
    Is it possible for a local minimum to be a global maximum? Similarly, is it possible for a local maximum to be a global minimum?
    No...because global means over the entire domain and for it to be a relative max it must be greater than some points to be a relative max...so it can't be greater than some to be a relative(local) max and be less than all to be an absolute(global)min
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  3. #3
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    Quote Originally Posted by casemeister View Post
    Is it possible for a local minimum to be a global maximum? Similarly, is it possible for a local maximum to be a global minimum?
    Only if all maximums equal all minimums, hence a flat line with no slope. However, you can argue that there are no maximums or minimums in that situation.
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    MCV4U is a course taken by secondary school students


    any test or quiz are needed

    Thanks
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