Hyperbola/1 to 2/Maximal lower staircase function with two steps/Exercise

We consider the function

$[1,2]\longrightarrow \mathbb {R} ,t\longmapsto g(t)={\frac {1}{t}}.$

1. Determine the area of the maximal lower staircase function for ${}g$ for an interval partitions of the form ${}1\leq x\leq 2$ in dependence on ${}x$.
2. Determine ${}x$ between ${}1$ and ${}2$, for which the area of the lower maximal staircase function for ${}g$ for an interval partition given by ${}1\leq x\leq 2$ is maximal. What is the value of the corresponding area?

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