determining the interval where the function is increasing\nusing only the values given in the table for the…

determining the interval where the function is increasing\nusing only the values given in the table for the function $f(x)=-x^{3}+4x + 3$, what is the largest interval of $x$-values where the function is increasing?\n|$x$|$f(x)$|\n|----|----|\n|$-3$|$18$|\n|$-2$|$3$|\n|$-1$|$0$|\n|$0$|$3$|\n|$1$|$6$|\n|$2$|$3$|

determining the interval where the function is increasing\nusing only the values given in the table for the function $f(x)=-x^{3}+4x + 3$, what is the largest interval of $x$-values where the function is increasing?\n|$x$|$f(x)$|\n|----|----|\n|$-3$|$18$|\n|$-2$|$3$|\n|$-1$|$0$|\n|$0$|$3$|\n|$1$|$6$|\n|$2$|$3$|

Answer

Explanation:

Step1: Check function values

Compare $f(x)$ values for consecutive $x$ - values.

Step2: Analyze intervals

For $x$ from - 1 to 1: $f(-1)=0$, $f(0)=3$, $f(1)=6$. Function is increasing as $f(x)$ values are rising. For other intervals, function is decreasing.

Answer:

$(-1,1)$