And when x=t, the extreme value is 0, that is, 4t? +4at? +bt=0
A=-2t b=4t can be expressed by two formulas simultaneously?
So f(x)=4x? -8tx? +4t? x=4x(x? -2tx+t? )=4x(x-t)?
So f(x)=0 has two solutions, 0 and t.
The figure enclosed by f(x) and x axis is a block from 0 to t.
Then the area t squared /3 can be obtained by integrating f(x) from 0 to t (definite integral).