Medium
According to the Mean Value Theorem,which of the following functions does not satisfy the conditions on the interval $[0, 1]$?
- A$f(x) = \begin{cases} \frac{1}{2} - x, & x < \frac{1}{2} \\ (\frac{1}{2} - x)^2, & x \ge \frac{1}{2} \end{cases}$
- B$f(x) = \begin{cases} \frac{\sin x}{x}, & x \ne 0 \\ 1, & x = 0 \end{cases}$
- C$f(x) = x |x|$
- D$f(x) = |x|$
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Examine the applicability of the Mean Value Theorem for the following functions:
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