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SOLUTION 3: We are given the function f(x)=x2x2/3 and the interval [1,8]. This function is continuous on the closed interval [1,8] since it is the sum of continuous functions y=x2 (polynomial) and y=x2/3=(x2)1/3 (the functional composition of continuous functions y=x2 and y=x1/3). The derivative of f is f(x)=2x(2/3)x1/3=2x23x1/3 We can now see that f is NOT differentiable on the open interval (1,8) since f is not defined at x=0. The assumptions of the Mean Value Theorem have NOT been met, so the Mean Value Theorem does not apply.

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