Find All Relative Extrema of the Function $f ( x ) = \sqrt { 36 - x ^ { 2 } }$

question 6

Multiple Choice

Find all relative extrema of the function $f ( x ) = \sqrt { 36 - x ^ { 2 } }$ . Use the Second-Derivative Test when applicable.

• A)The relative minimum is \(( 0,6 )\) and the relative maximum is \(( - 6,0 )\) .
• B)The relative maximum is \(( 0,6 )\) .
• C)The relative minimum is \(( 0,6 )\) .
• D)The relative maximum is \(( 0,6 )\) and the relative minima are \(( 6,0 )\) and \(( - 6,0 )\) .
• E)The relative minimum is \(( 0,6 )\) and the relative maximum is \(( 6,0 )\) .

---

Definitions:

Emotional Support

Assistance given to someone, typically providing reassurance, acceptance, and encouragement during times of stress.

Autonomous

The capacity to make decisions independently, free from external control or influence, often highlighting self-governance.

Orienting Principles

Fundamental concepts or assumptions that guide thinking, research, or policy in various fields.

Therapeutic Factor

An element or aspect of therapy that contributes to the healing process or beneficial outcomes for the person receiving treatment.