Suppose fff is a continuous function on [0,1][0, 1][0,1] and g(x)=maxt∈[0,x]f(t)g(x) = \max_{t \in [0, x]} f(t)g(x)=maxt∈[0,x]f(t). Which property must g(x)g(x)g(x) satisfy?
g(x) is always differentiable.
g(x) is monotonically non-decreasing.
g(x) is identical to f(x).
g(x) must be a constant function.