Question

x | f(x)
-4 | 16
-3 | -2
-2 | 0
-1 | 6
0 | 0
1 | -2

a local maximum of the function f(x) occurs for which x-value?

options: -3, -1, -4, -2

Explanation:

Step1: Analyze function values

Check \( f(x) \) values: \( f(-4)=16 \), \( f(-3)=-2 \), \( f(-2)=0 \), \( f(-1)=6 \), \( f(0)=0 \), \( f(1)=-2 \).

Step2: Identify local maximum

A local maximum at \( x = a \) means \( f(a) \geq f(x) \) for nearby \( x \). For \( x=-4 \), \( f(-4)=16 \) is greater than adjacent \( f(-3)=-2 \), and larger than other values (16 > 6, 16 > 0, etc.).

Answer:

\( -4 \) (corresponding to the option with \( x = -4 \))