Question

find the minimums and maximum points of x+sin(x)

Answer 1

At a maximum point, \(f '(x)\) changes sign from + to − .
At a minimum point, \(f '(x)\) changes sign from − to +

Since \(f(x)+x+\sin (x), ~f'(x) = 1+\cos(x)\)

Does \(1+\cos x\) cross x-axis?

Answer 2

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Answer 3

no it doesn't cross the x axis

Answer 4

Yeah, it never cross x-axis, so that mean there is no extremum point.