Question

The derivative of \(f(x) = 3|2 + x|\) at the point \(x_0 = -3\) is

• A. 3
• B. -3
• C. 0
• D. None of the above

Hint:

\(\frac{d}{dx}|x| = \frac{x}{|x|}\) for \(x \neq 0\).

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
Derivative of \(|x|\) is \(x/|x|\) for \(x \neq 0\).
Step 2: Detailed Explanation:
\(f(x) = 3|x + 2|\)
At \(x = -3\), \(x + 2 = -1<0\), so \(|x + 2| = -(x + 2)\)
\(f(x) = -3(x + 2)\)
\(f'(x) = -3\)
Step 3: Final Answer:
Derivative is \(-3\).