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

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設(shè)箱子底邊為x,高為y則根據(jù)題意 得 x^2*y=62,5材料的用料為x^2+4*x*y,現(xiàn)求其最小值解如下:將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當(dāng)x^2=125/x時,即x=5,則y=2,5時,上式等號成立,而此時的用料為最小值