Consider the function f:R→R defined by .fx=2−sin1x  x,   x≠0         0                        ,   x=0 Then  f is:

f(x)=2x-xsin1x x>0-2x+xsin1x x<0f'(x)=2+1xcos1x-sin1x                           x>0-2-1xcos1x-1sin1x                        x<0f'(x)=>0x>0<0x<0The function is non monotonic in the interval −∞,0  &   0,∞