1929年(昭和4年)京都帝國大學工學部-數學(全3問)

[1] Find the inflexion point of a curve,

where is positive and smaller than .

[2] Determine the ration of the depth to the inner diameter of an open cylindrical vessel, to make the necessary material minimum, for a given capacity when the base and the side are of equal thickness .

[3] Thr surface of water in a rotating cylinder about its vertical axis a paraboloid of revolution. Find the lowest depth of the water, when the inner diameter , the volume of the water and the maximum difference of the height are given.