let f be a continuous density which is zero outside in the interval[0,A]

,where A >0, let F be the corresponding cdf.

a) prove that there exists at least one point X such that f(x)=1/A

b), let 0<p<1 prove there exists at least one point Xp such that Xp is the pth quantile of the distribution defined by f and F, give an example to show that the point Xp may not be unique.

Thanks a lot!!