I am interested in Optimal Control:
https://en.wikipedia.org/wiki/Optimal_control
and I am reading the discrete example at the bottom of the Wikipedia page:
where they give the solution as:

I have some questions (from top red annotations to bottom):
- Where does ($\lambda_{t+1} u_t$) come from?
- How did they equate negative the differential, to $-(\frac{u_t}{x_t})^2$ ?
- What does it mean using the initial and turn T conditions?
