Consider the function f (x) = x^{2/3} on the interval [-1,8].

Determine whether or not f (x) satisfies the conditions of the Mean Value Theorem for its given interval. Select the most correct answer from the choices below:

(a). The Mean Value Theorem applies for f (x) on [-1,8].

(b). The Mean Value Theorem does not apply since f (x) is not continuous on [-1,8].

(c). The Mean Value Theorem does not apply since f (x) is not differentiable on (-1,8).

(d). The Mean Value Theorem does not apply since f (x) is not continuous on [-1,8] and not differentiable on (-1,8)

Question

Mathematics

Serenity Cordova

14 November, 09:05

Consider the function f (x) = x^{2/3} on the interval [-1,8].

Determine whether or not f (x) satisfies the conditions of the Mean Value Theorem for its given interval. Select the most correct answer from the choices below:

(a). The Mean Value Theorem applies for f (x) on [-1,8].

(b). The Mean Value Theorem does not apply since f (x) is not continuous on [-1,8].

(c). The Mean Value Theorem does not apply since f (x) is not differentiable on (-1,8).

(d). The Mean Value Theorem does not apply since f (x) is not continuous on [-1,8] and not differentiable on (-1,8)

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Answers (1)

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Colten · Answer 1

The right option is (c). The Mean Value Theorem does not apply since f (x) is not differentiable on (-1,8). Because the derivative of f is 2/3 x^ (-1/3) which is undefined at x=0. So, that would imply that it is not differentiable along the interval.