Final answer:
The statement that is true about the function f(x) = x² + 2x is that it has neither absolute minimum nor absolute maximum.
Step-by-step explanation:
The statement that is true about the function f(x) = x² + 2x is option B) It has neither absolute minimum nor absolute maximum.
To find the absolute minimum and absolute maximum of a function, we need to determine the critical points where the derivative of the function is either equal to zero or undefined. In this case, the derivative of f(x) is 2x + 2. Setting this equal to zero, we find x = -1 as the critical point.
Since f'(x) = 2x + 2 is always positive for x > -1 and always negative for x < -1, we conclude that there is no absolute minimum or absolute maximum for the given function. Therefore, option B is the correct choice.