1929　京都帝国大学　工学部

【１】 Find the inflexion point of a curve,

$y=l({\displaystyle \frac{x}{l}}-{\displaystyle \frac{3x^3}{l^3}}+{\displaystyle \frac{2x^4}{l^4}})$

where $x$ is pssitive and smaller than $l\text{.}$

【２】 Determine the ratio of the depth $h$ to the inner diameter $d$ of an open cylindrical vessel, to make the necessary material minimum for a given capacity $A$ when the base and the side are of equal thickness $t\text{.}$

【３】 The surface of water in a rotating cylinder about its vertical axis is a paraboloid of rebolution. Find the lowest depth $a$ of the water, when the inner diameter $2r\text{,}$ the volume $V$ of the water and the maximum difference $h$ of the height are given.