Question

use the table to describe the intervals over which ( f(x) = 15x^2 ) is increasing and decreasing.

( x )	( f(x) = 15x^2 )	( (x, y) )
( -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 ( x > 0 )
(simplify your answer. type an inequality.)

the function ( f(x) ) is decreasing over the interval ( square )
(simplify your answer. type an inequality.)

Explanation:

Step1: Analyze the function's behavior from the table

Looking at the table values: when \( x \) goes from -2 to 0 (i.e., \( x \) is negative and increasing towards 0), \( f(x) \) values go from 60 to 15 to 0, which means \( f(x) \) is decreasing as \( x \) increases in this negative to 0 range. When \( x \) is less than 0 (moving from more negative to 0), the function value decreases as \( x \) increases (since for \( x=-2, f(x)=60 \); \( x = -1, f(x)=15 \); \( x = 0, f(x)=0 \)). So the function is decreasing when \( x \) is less than 0.

Step2: Formulate the inequality for decreasing interval

From the analysis, the function \( f(x) = 15x^2 \) is decreasing when \( x < 0 \).

Answer:

\( x < 0 \)