SOLUTION: Does the function f(x) = x/x^2-1 for -2 =< x= <2 satisfy the hypothesis of the Extreme Value Theorem? Please give a reason for your answer.

Question 1171193: Does the function f(x) = x/x^2-1 for -2 =< x= <2 satisfy the hypothesis of the Extreme Value Theorem? Please give a reason for your answer.
Answer by ikleyn(52781) (Show Source): You can put this solution on YOUR website!
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    In calculus, the Extreme Value Theorem states that if a real-valued function f is continuous on 

    the closed interval [a,b], then f must attain a maximum and a minimum, each at least once.

See this Wikipedia article
https://en.wikipedia.org/wiki/Extreme_value_theorem

So, the function is assumed to be CONTINUOUS.

But the given function is not continuous : it has singular points at x = -1 and x= 1 inside the interval [-2,2].

So, it does not satisfy the condition of the theorem.

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Explained and completed.

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