We never showed that the value found in computing the optimal t with the Marginal Value Theorem is in fact a maximum. For each of the following forms for the function F(t), find the second derivative of R(t) and the point where F'(t) = F(t) / t + τ and check whether the solution is a maximum.
1. Suppose F(t) = t / 1 + t and travel time is τ = 1.
2. Suppose F(t) is any function with F"(t) < 0 and travel time is τ = 1.