Which one of the following functions is differentiable at $x=0$ ?

A ball is thrown vertically upwards with an initial speed $u$ from a height $h$ above the ground. The ball eventually hits the ground with a speed $v$. The acceleration due to gravity is $g$ and air resistance is negligible. What is the average speed of the ball over its entire trajectory?

Two cubes $A$ and $B$ of same dimensions are made of different materials with densities $\rho_A$ and $\rho_{\mathrm{B}}$, respectively. Cube A floats in water with a fraction $\eta$ of its volume immersed. When cube $B$ is placed on top of cube $A$, it is found that cube $A$ is just entirely immersed, while cube $B$ is entirely above the surface of the water. What is the ratio $\rho_{\mathrm{B}} / \rho_{\mathrm{A}}$ ?

An object is placed in front of a convex lens. A real inverted image of double its size is formed. When the object is moved closer to the lens by a distance $d$, the image shifts away from the lens by a distance $8 d$ from its previous position. What is the magnitude of the magnification in the final setup?