Consider the function g(x)= cases x^ 2 -2, & -2 x<1, 3-x, & 1 x 4
MATHEMATICS · Single correct · A Level · Mathematics · Differentiation · Differentiation
Problem
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].