Does h(x)=5+(5/5-x) have an absolute maximum and absolute minimum on [3,6]? If so, what are they? If not, please explain in terms of the max-min theorem. (or extreme value theorem)
For a max/min there is a horizontal tangent with the derivative =0 or undefined at a cusp.
h(x)=5+5/(5-x)
h'(x) = 5/(5-x)^2
It is never = 0 and is undefined only at x=5 which is not a cusp
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