- #1
peripatein
- 868
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Hi,
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.
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?
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?