Question

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

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

Hint:

If \( f'(x) \ge m \): Function grows at least linearly. Use \( f(b) \ge f(a) + m(b-a) \).

Answer 1

The Correct Option is B