Thread: Calculus, Local and global extrema

1. 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?

2. Originally Posted by casemeister
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

3. Originally Posted by casemeister
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.

4. MCV4U is a course taken by secondary school students

any test or quiz are needed

Thanks