Consider the function g(x)=25−x2 defined on the closed interval [−5,5].
a. (i) State the domain of g and identify the endpoints of the interval under consideration.
b. (ii) Determine whether there exist any points in (−5,5) at which g′(x)=0. Justify your answer without performing explicit derivative calculations.
c. (iii) Using clear reasoning, identify the points in [−5,5] where g attains its absolute maximum and absolute minimum values. State these maximum and minimum values.