Suppose a Single-Input Production Function Has Initially Increasing but Eventually

Suppose a single-input production function has initially increasing but eventually decreasing marginal product -- and suppose we know that an interior solution is profit maximizing.In this case,the first order condition for the profit maximization problem
a.
is necessary for identifying the profit maximizing production plan.
b.
is sufficient for identifying the profit maximizing production plan.
c.
is both necessary and sufficient for identifying the profit maximizing production plan.
d.
is neither necessary nor sufficient for identifying the profit maximizing production plan.