Math  /  Calculus

QuestionDoes Lagrange's mean value theorem apply to f(x)=x1/3f(x)=x^{1/3} on [1,1][-1, 1]? What can we conclude?

Studdy Solution
Since the function is not differentiable on the entire open interval (1,1)(-1,1), the Lagrange's Mean Value Theorem does not apply to the function f(x)=x1/3f(x)=x^{1 /3} on the interval [1,1][-1,1].
So, the conclusion is that the Lagrange's Mean Value Theorem does not apply to the function f(x)=x1/3f(x)=x^{1 /3} on the interval [1,1][-1,1] because the function is not differentiable on the entire open interval (1,1)(-1,1).

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