find the absolute minimum and absolute maximum for the given funtion f(x)=x-2sinx between 0 and 2(pi)

Question

find   the  absolute   minimum  and   absolute    maximum    for   the   given   funtion  f(x)=x-2sinx  between   0  and  2(pi)

anonymous · Answer

PLS   GIVE   A   SIMFILICATION  TO   SOLVE   THE   PROBLEM

zehanz · Answer

Use the derivative:$$f'(x)=1-2\cos x$$Solve the equation:$$f'(x)=0 \Leftrightarrow 1-2\cos x = 0 \Leftrightarrow \cos x = \frac{ 1 }{ 2 }$$There are two solutions in [0, 2pi].
These are the x-values where f has a (local) extreme.
You can calculate the extremes by substituting the solutions of f' in f.
Also calculate f(0) and f(2pi) to get the extremes in the endpoints.
If you have all the extremes, you can decide what the absolute maximum and minimum values are.