an open rectangular box whit a square base is to be constructed so that its volume is nd the dimensions of box so that the area of the materialused in its construction is a ow that this area is a minimum and not a maximum
热心网友
设箱子底边为x,高为y则根据题意 得 x^2*y=62,5材料的用料为x^2+4*x*y,现求其最小值解如下:将y=62,5/x^2代入上式得x^2+4*x*y=x^2+4*x*(62,5/x^2)=x^2+250/x=x^2+125/x+125/x =x^2*(125/x)*(125/x)=125*125=15625当x^2=125/x时,即x=5,则y=2,5时,上式等号成立,而此时的用料为最小值