Question

determining the interval where the function is increasing
using 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?

$x$	$f(x)$
-3	18
-2	3
-1	0
0	3
1	6
2	3

Explanation:

Step1: Recall increasing - function definition

A function $y = f(x)$ is increasing if $f(x_1)

Step2: Analyze the table values

When $x=-3$, $f(-3)=18$; when $x = - 2$, $f(-2)=3$ (decreasing). When $x=-2$, $f(-2)=3$; when $x=-1$, $f(-1)=0$ (decreasing). When $x=-1$, $f(-1)=0$; when $x = 0$, $f(0)=3$ (increasing). When $x = 0$, $f(0)=3$; when $x=1$, $f(1)=6$ (increasing). When $x = 1$, $f(1)=6$; when $x=2$, $f(2)=3$ (decreasing).

Step3: Determine the increasing interval

The function is increasing for $x$ values from $- 1$ to $1$.

Answer:

$(-1,1)$