NOT too hard for parents here. IT is essentially the only soluti

IT is essentially the only solution, recaptured here.

1) f(x)=x(x-1) in (0, 1] is a parabola, intercepting the x-axis at the endpoints x=0 and x=1 (opening upward, just below the x-axis). It's vertex is at x=1/2 (middle of the interval) with minimum y-value  of -1/4.

HINT: The graph of any quadratic function is a parabola. The sign of the coefficient of the leading term determines whether it is opening up or down.

2). The minimum of f(x) in the 2nd interval (1, 2] is -1/2 when x = 3/2; the minimum of f(x) in the 3nd interval (2, 3] is -1 when x = 5/2.

3). With choices C and D ruled out, B is correct because f(7/3)=4*f(1/3)=-8/9 ( f(x) is decreasing decreasing from 2 until 5/2, then increasing until 3).