# Judge the following is true or false If f is continuous on ( 0,1 ) then there is a c in (0,1) such that f(c) is a maximum value of f on (0,1)?

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my friend tell me answer is true

but I think it is wrong

because according to the "Extreme Value Theorem"

the interval {a,b} should be "closed"

maximum is possible to be found

Is my thought wrong ?

my friend tell me answer is true

but I think it is wrong

because according to the "Extreme Value Theorem"

the interval {a,b} should be "closed"

maximum is possible to be found

Is my thought wrong ?

##### 1 Answer

Jun 21, 2016

#### Answer:

False

#### Explanation:

As you believed, the interval would need to be closed for the statement to be true. To give an explicit counterexample, consider the function