Question

Let \( f \) be a function which is differentiable for all real \( x \). If \( f(2) = -4 \) and \( f'(x) \geq 6 \) for all \( x \in [2, 4] \), then:

• A. \( f(4)<8 \)
• B. \( f(4) \geq 12 \)
• C. \( f(4) \geq 8 \)
• D. \( f(4)<12 \)

Hint:

For differentiable functions, use the Mean Value Theorem to relate the derivative to the function's change over an interval. Ensure the derivative bound is applied correctly to determine the range of \( f(b) \).