Question

What is the behavior of f'(x) if f''(x) > 0?

a) Decreasing
b) Need more information
c) Increasing
d) Stationary

Answer 1

If f''(x) > 0, the behavior of f'(x) is either increasing or stationary.

Step-by-step explanation:

If f''(x) > 0, it means that the second derivative of the function is always positive. The behavior of f'(x), the first derivative of the function, depends on the concavity of the function. If f''(x) > 0, the function is concave up, which means that it is always increasing or zero. Therefore, the behavior of f'(x) is either increasing or stationary, depending on whether the function is increasing or constant.

So, the correct answer is d) Stationary.