`P=x(4-x)`

`=4x-x^2`

`=-x^2+4x`

`=-x^2+4x-4+4`

`=(-x^2+4x-4)+4`

`=-(x^2-4x+4)+4`

`=-(x^2-2*x*2+2^2)+4`

`=-(x-2)^2+4`

Vì: `(x-2)^2>=0\AAx`

(bình phương luôn không âm)

Suy ra: `-(x-2)^2<=0\AAx`

`->P=-(x-2)^2+4<=0+4=4\AAx`

`->P_(max)=4`

Dấu "=" xảy ra: `x-2=0->x=2`

Vậy: `P_(max)=4` khi `x=2`