(Solved): Suppose that \( f \) is given for \( x \) in the interval \( [0,12] \) by A. Estimate \( f^{\prime} ...

Suppose that \( f \) is given for \( x \) in the interval \( [0,12] \) by A. Estimate \( f^{\prime}(2) \) using the values of \( f \) in the table. \( f^{\prime}(2) \approx \) B. For what values of \( x \) does \( f^{\prime}(x) \) appear to be positive? (Give your answer as an interval or a list of intervals, e.g., (-infinity, 8\( ] \) or \( (1,5),(7,10) \).) C. For what values of \( x \) does \( f^{\prime}(x) \) appear to be negative? (Give your answer as an interval or a list of intervals, e.g., (-infinity, 8\( ] \) or \( (1,5),(7,10) \).)