由y= f'( x)的图像知,f(x)在[1,3)单调减,在(3,+∞)单调增,又f( 4)= f( 2)= 1,画图,
则2≤2x+y≤4,再结合x≥0,y≥0,画图,S=1/2×2×4-1/2×1×2=3