A function p is given by
p(x)=⎩⎨⎧x1,0,x=0x=0
for x in the closed interval [−3,3]. Which statement correctly explains why the Extreme Value Theorem does NOT guarantee that p attains an absolute maximum on [−3,3]?
a) The interval [−3,3] is not open, and the Extreme Value Theorem applies only to open intervals
b) p is not continuous at x=0, so a required hypothesis fails
c) p is unbounded on [−3,3], and the theorem requires the function to be bounded
d) p is not differentiable at x=0, and differentiability is required by the theorem