F''(x)>0 in [a,b] so f has a maximum at a or b.

  • Thread starter peripatein
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  • #1
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Hi,

Homework Statement


I was asked to show that if f''(x)>0 for every x in [a,b], then f has a maximum at either a or b.


Homework Equations





The Attempt at a Solution


The book proves it thus:
If f has a sationary point in [a,b] then that point must be a minimum, as f''(x)>0, hence a maximum must be obtained at either a or b.
If f does not have a stationary point in [a,b], then f is increasing or decreasing in [a,b] and hence a maximum must be obtained at either a or b.

I don't understand both "hence a maximum must be obtained at either a or b" and "then f is increasing or decreasing in [a,b] and hence a maximum must be obtained at either a or b".
Could someone please clarify?
 

Answers and Replies

  • #2
880
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I believe I've got it, thanks anyway :-)
 

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