Answer:
I) Joe would be considered a fiduciary for the trust account.
IV) Joe would be considered to have a certain level of discretionary authority over the trust account and would have custody of trust account funds as trustee.
Explanation:
Since the client named Joe as his trustee, once the client passes away Joe will be in charge of managing the trust account. Since Joe must place the interests of the beneficiaries (the client's children) ahead of his own interests, Joe is considered a fiduciary for the trust account.
Joe is also in charge of managing the investments, therefore he will have discretionary authority over them. Since Joe is the trustee, he has control of the money and he can also have custody of the funds.