-cos(x)-x has the derivative sin(x)-1 which is zero when x=π/2 and 2πn+π/2 where n is an integer. If x is in [0,2π], x=π/2 is the only value in this interval. cos(x)=0 for this value of x, so the function has the value -π/2, and the point (π/2,-π/2) is an inflection. As x increases the function decreases and the point of inflection represents a temporary stationary condition where the curve is flat.