E-IN04 · Every point versus at least one point
Let \(F(x)=2x^2-12x+10\). A closed interval \([h,h+2]\) moves along the x-axis.
Solve \(F(x)\lt 0\).
Find all \(h\) for which \(F(x)\lt 0\) for every \(x\in[h,h+2]\).
Find all \(h\) for which there is at least one \(x\in[h,h+2]\) with \(F(x)\lt 0\).
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