# How do you verify whether rolle's theorem can be applied to the function #f(x)=x^3# in [1,3]?

When we are asked whether some theorem "can be applied" to some situation, we are really being asked "Are the hypotheses of the theorem true for this situation?"

(The hypotheses are also called the antecedent, of 'the if parts'.)

So we need to determine whether the hypotheses of Rolle's Theorem are true for the function

Rolle's Theorem has three hypotheses:

We say that we can apply Rolle's Theorem if all 3 hypotheses are true.

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To verify if Rolle's Theorem can be applied to the function (f(x) = x^3) on the interval ([1,3]), you need to check two conditions:

**Continuity**: Ensure that (f(x)) is continuous on the closed interval ([1,3]).**Differentiability**: Verify that (f(x)) is differentiable on the open interval ((1,3)).

If both conditions are met, you can conclude that Rolle's Theorem can be applied.

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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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