All the options are either true or false

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【General guidance】The answer provided below has been developed in a clear step by step manner.Step1/8We need to check True and False .I. True, An absolute maximum of a function f(x) is the largest value of all the y-values of f on the domain of f .Explanation:Please refer to solution in this step.Step2/8II. False, A function has one absolute maximum if exist , since we have absolute maximum of f is \( \begin{align*} \mathrm{{M}} &\ge \mathrm{{y},\forall{x}\Rightarrow{y}={f{{\left({x}\right)}}}.} &\text{(1)} \end{align*} \)So Absolute maximum is unique if it is exist.Explanation:Please refer to solution in this step.Step3/8III. True, A local maximum \( \mathrm{{f{{\left({c}\right)}}}} \)of function \( \mathrm{{f{{\left({x}\right)}}}} \) is the values as \( \mathrm{{f{{\left({c}\right)}}}\ge{y},\forall{x}} \) such that \( \mathrm{{x}\in{\left({c}-\delta,{c}+\delta\right)}} \) for small number \( ... See the full answer