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local max/min #952

Closed pfatheddin closed 3 months ago

pfatheddin commented 3 months ago

See maximumsAndMinimums/exercises/maxMinTrueFalse2.tex

https://ximera.osu.edu/mooculus/maximumsAndMinimums/exercises/exerciseList/maximumsAndMinimums/exercises/maxMinTrueFalse2

I am not sure about this statement. Based on first derivative test we either have increasing then decreasing to get local max or decreasing then increasing to get local min. The example in hint has derivative 0 so it is not positive or negative and the constant horizontal line y=5 doesn’t have a local max or min since it is not increasing or decreasing.

bwramsey commented 3 months ago

For the constant function f(x)=5, EVERY point is both a local maximum and a local minimum. Please review the definitions in the book.

pfatheddin commented 3 months ago

yes the definition is f(x_0)\leq f(x) for all x in the neighborhood of x_0 for local min so by definition every point is a local min. But this at this stage can be confusing. But I will leave it to you.