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- Feb 20th 2011, 06:29 AMmariamaMax - Min theorm ( please help me to solve this problem)
- Feb 20th 2011, 08:04 AMHallsofIvy
You have given two problems with no sign that you have tried anything yourself. You should know from reading the forum rules that you must give some attempt yourself. In addition, that helps us know what kind of help you need.

The first problem asks for a value of a that will make the given function continuous. Do you know the definition of "continuous"? How does it apply to this problem?

The second problem asks about the "Max-min theorem". What does that theorem say? - Feb 20th 2011, 08:13 AMmariama
Yes , I know the definition of continuous functions .

but how can i know if the function has a max. or min value on the interval

Max-Min theorem says :

if f(x) is cont. on the closed interval [a,b], then there exist numbers p,q in the interval [a,b] such that for all x in [a,b]

f(p) less than or equal to f(x) less that or equal to f(q)

Thus f has the absolute min. value m=f(p) taken on at the point p , and the absolute max. value M =f(q)