(a) Use the function (x) = Ax (a-x) (for 0 < x < a, otherwise 0) to get an upper bound on the ground state

(a) Use the function Ψ(x) = Ax (a-x) (for 0 < x < a, otherwise 0) to get an upper bound on the ground state of the infinite square well.
(b) Generalize to a function of the form Ψ(x) = A[x (a-x)]^P, for some real number p. What is the optimal value of p, and what is the best bound on the ground state energy? Compare the exact value.