Attention curve/-x^2+25x-100/Optimum of 8 to 18/Exercise

According to recent studies, the student's attention skills during the day are described by the following function

$[8,18]\longrightarrow \mathbb {R} ,x\longmapsto f(x)=-x^{2}+25x-100.$

Here, ${}x$ is the time in hours and ${}y=f(x)$

is the attention,n measured in micro-credit points per second. When should one start a one and a half hour lecture, such that the total attention skills are optimal? How many micro-credit points will be added during this lecture?

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