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math gurus .....please 1 Question

tiger88

New member
Which is false?
a) A continuous function on a closed interval must attain an absolute maximum and an absolute minimum value on the closed interval.
b) A continuous function on an open interval must attain either an absolute maximum or an absolute minimum value on the closed interval.
c) A continuous function on an open interval does not necessarily attain either an absolute maximum or an absolute minimum value on the closed interval.
d) A continuous function on a closed interval may have more than one location where it attains an absolute maximum and an absolute minimum value on the closed interval.

??

karma for answer and a tiger88 hug :D
 
tiger88 said:
Which is false?
a) A continuous function on a closed interval must attain an absolute maximum and an absolute minimum value on the closed interval.
b) A continuous function on an open interval must attain either an absolute maximum or an absolute minimum value on the closed interval.
c) A continuous function on an open interval does not necessarily attain either an absolute maximum or an absolute minimum value on the closed interval.
d) A continuous function on a closed interval may have more than one location where it attains an absolute maximum and an absolute minimum value on the closed interval.

??

karma for answer and a tiger88 hug :D

B is false. A and D are proved by Weierstrass theorum while C fails to meet the assumptions of the theorum.
 
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