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

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)

anonymous · Answer

C right

amistre64 · Answer

what makes you think its not differentiable?

amistre64 · Answer

we know its continuous, so the only question is if its differentiable ...

amistre64 · Answer

the question remains as to why they may be right

anonymous · Answer

Not in the interval, correct?

amistre64 · Answer

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