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Over what interval is the function shown in the table decreasing?
inequality number Sign





x^(¨)

f(x)=3x^(2)

(x,y)


-2
12

(-2,12)


-1
3

(-1,3)


0
0

(0,0)


1
3

(1,3)


2
12

(2,12)

Over what interval is the function shown in the table decreasing?\newlineinequality number Sign\newline\begin{tabular}{|r|r|c|}\newline\hline \multicolumn{11}{|c|}{x¨ \ddot{x} } & f(x)=3x2 f(x)=3 x^{2} & (x,y) (x, y) \\\newline\hline2-2 & 1212 & (2,12) (-2,12) \\\newline\hline1-1 & 33 & (1,3) (-1,3) \\\newline\hline 00 & 00 & (0,0) (0,0) \\\newline\hline 11 & 33 & (1,3) (1,3) \\\newline\hline 22 & 1212 & (2,12) (2,12) \\\newline\hline\newline\end{tabular}

Full solution

Q. Over what interval is the function shown in the table decreasing?\newlineinequality number Sign\newline\begin{tabular}{|r|r|c|}\newline\hline \multicolumn{11}{|c|}{x¨ \ddot{x} } & f(x)=3x2 f(x)=3 x^{2} & (x,y) (x, y) \\\newline\hline2-2 & 1212 & (2,12) (-2,12) \\\newline\hline1-1 & 33 & (1,3) (-1,3) \\\newline\hline 00 & 00 & (0,0) (0,0) \\\newline\hline 11 & 33 & (1,3) (1,3) \\\newline\hline 22 & 1212 & (2,12) (2,12) \\\newline\hline\newline\end{tabular}
  1. Determine Decreasing Intervals: To determine where the function is decreasing, we need to look at the values of f(x)f(x) as xx increases and find where f(x)f(x) is getting smaller.
  2. Interval 2-2 to 1-1: Looking at the table, from x=2x = -2 to x=1x = -1, f(x)f(x) changes from 1212 to 33. This means the function is decreasing in this interval.
  3. Interval 1-1 to 00: From x=1x = -1 to x=0x = 0, f(x)f(x) changes from 33 to 00. The function continues to decrease.
  4. Interval 00 to 11: From x=0x = 0 to x=1x = 1, f(x)f(x) changes from 00 to 33. Here, the function starts increasing.
  5. Overall Decreasing Interval: Since the function is only decreasing from x=2x = -2 to x=0x = 0, the interval over which the function is decreasing is from 2-2 to 00.

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