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## 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?