part 1 of 2 use the table to describe the int...
part 1 of 2 use the table to describe the intervals over which f(x)=15x² is increasing and decreasing. x f(x)=15x² (x,y) -2 60 (-2,60) -1 15 (-1,15) 0 0 (0,0) 1 15 (1,15) 2 60 (2,60) the function f(x) is increasing over the interval . (simplify your answer. type an inequality.)
Answer
# Explanation:
## Step1: Recall increasing - decreasing property
A function $y = f(x)$ is increasing if for $x_1<x_2$, $f(x_1)<f(x_2)$ and decreasing if for $x_1 < x_2$, $f(x_1)>f(x_2)$.
## Step2: Analyze the given table values
When $x$ goes from - 2 to - 1, $f(x)$ goes from 60 to 15 (decreasing). When $x$ goes from - 1 to 0, $f(x)$ goes from 15 to 0 (decreasing). When $x$ goes from 0 to 1, $f(x)$ goes from 0 to 15 (increasing). When $x$ goes from 1 to 2, $f(x)$ goes from 15 to 60 (increasing).
## Step3: Determine the increasing interval
The function $f(x)=15x^{2}$ is increasing for $x\geq0$.
# Answer:
$x\geq0$