A tennis ball is released from a height h and after freely falling it rebounds on a wooden floor and reaches height $\frac{h}{2}.$ The velocity versus height of the ball during its motion may be represented graphically by (graph are drawn schematically and on not to scale)

At height $h$ velocity of the ball is zero. The velocity at ground (means zero height) is nonzero therefore option (A) is incorrect and velocity versus height is non-linear therefore option (B) is also incorrect. The speed of the ball at height $h$ is given by, $v^2=2gh$

$v\frac{dv}{dh}=2g=\text{constant}\Rightarrow \frac{dv}{dh}=\frac{\text{constant}}{v}$

Here we can see slope is large when velocity is low therefore at Maximum height the slope should be very large which is in option (C) and as velocity increases slope must decrease there for option (C) is correct.