Consider the function
g(x)={x2−2,3−x,−2≤x<1,1≤x≤4.
Which of the following statements about the existence of absolute extrema of g on the closed interval [−2,4] is true?
a) g is not differentiable at x=1, so the Extreme Value Theorem cannot be applied on [−2,4].
b) Any absolute extremum of g must occur at a point where g′(x)=0, so only interior critical points need to be examined.
c) g is not continuous on [−2,4], so the Extreme Value Theorem does not guarantee absolute extrema.
d) Since g is discontinuous at x=1, it cannot have an absolute maximum or minimum on [−2,4].