# For what values of x is #f(x)=(4x)/(x^2-1)# concave or convex?

graph{(4x)/(x^2-1) [-10, 10, -5, 5]}

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The function ( f(x) = \frac{4x}{x^2-1} ) is concave for ( x \in (-1, 0) \cup (1, \infty) ) and convex for ( x \in (-\infty, -1) \cup (0, 1) ).

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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