Q. Over what interval is the function shown in the table decreasing?inequality number Sign\begin{tabular}{|r|r|c|}\hline \multicolumn{1}{|c|}{x¨} & f(x)=3x2 & (x,y) \\\hline−2 & 12 & (−2,12) \\\hline−1 & 3 & (−1,3) \\\hline 0 & 0 & (0,0) \\\hline 1 & 3 & (1,3) \\\hline 2 & 12 & (2,12) \\\hline\end{tabular}
Determine Decreasing Intervals: To determine where the function is decreasing, we need to look at the values of f(x) as x increases and find where f(x) is getting smaller.
Interval −2 to −1: Looking at the table, from x=−2 to x=−1, f(x) changes from 12 to 3. This means the function is decreasing in this interval.
Interval −1 to 0: From x=−1 to x=0, f(x) changes from 3 to 0. The function continues to decrease.
Interval 0 to 1: From x=0 to x=1, f(x) changes from 0 to 3. Here, the function starts increasing.
Overall Decreasing Interval: Since the function is only decreasing from x=−2 to x=0, the interval over which the function is decreasing is from −2 to 0.
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