`f(x) = x^(2/3) - 1, [-8,8]` Determine whether Rolle’s Theorem can be applied to `f` on the closed interval `[a, b]`. If Rolle’s Theorem can be applied, find all values of `c` in the open...

`f(x) = x^(2/3) - 1, [-8,8]` Determine whether Rolle’s Theorem can be applied to `f` on the closed interval `[a, b]`. If Rolle’s Theorem can be applied, find all values of `c` in the open interval

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Chapter 3, 3.2 - Problem 13 - Calculus of a Single Variable (10th Edition, Ron Larson).
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mathace | (Level 3) Assistant Educator

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Given: f(x)=x^(2/3)-1,[-8,8].

Rolle's Theorem does not apply to the function f(x) on the given interval because all 3 conditions of Rolle's Theorem will not be met.

The function f(x) is continuous on the closed interval [-8,8].

The function f(x) is not differentiable on the open interval (-8, 8). The function is not differentiable at x=0.

f(-8)=f(8)=3.

Because all 3 conditions are NOT met Rolle's Theorem does NOT apply.

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