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

We consider the function

$[1,2]⟶ℝ,t⟼g(t)=\frac{1}{t}.$

1. Determine the area of the maximal lower staircase function for $g$ for an interval partitions of the form $1\le x\le 2$ 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 $1\le x\le 2$ is maximal. What is the value of the corresponding area?

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