Question

If \( f(2) = 4 \) and \( f'(2) = 1 \), then \[ \lim_{x \to 2} \frac{x f(2) - 2f(x)}{x - 2} \text{ is equal to:} \]

• A. 0
• B. \( \frac{1}{2} \)
• C. 1
• D. 2

Hint:

The difference quotient \( \frac{f(x) - f(a)}{x - a} \) represents the derivative \( f'(a) \).

Answer 1

The Correct Option is D

Step 1: Use limit and derivative. We use the fact that \( f'(x) \) is the derivative of \( f(x) \). The given expression can be rewritten as a difference quotient, which represents the derivative at \( x = 2 \).
Step 2: Conclusion. Thus, the value of the given expression is 2.