(e) 2 minutes remaining \( \varnothing \) Let \( f(x) \) be a twice-differentiable function. If \( f^{\prime}(x)>0 \), then it must be that \( f^{\prime \prime}(x)>0 \). A True (B) False

The statement is (B) False. The fact that \( f'(x) > 0 \) means that the function \( f(x) \) is increasing at that point. However, this does not necessarily imply that the second derivative \( f''(x) \) is also positive. For example, consider the function \( f(x) = x^3 \). The first derivative is \( f'(x) = 3x^2 \), which is positive for \( x > 0 \). However, the second derivative is \( f''(x) = 6x \), which is positive for \( x > 0 \) but zero at \( x = 0 \) and negative for \( x < 0 \). Thus, \( f'(x) > 0 \) does not guarantee that \( f''(x) > 0 \).