Final answer:
The value of the integral of f''(x) from 1 to 4 is 0, since the derivative f'(x) is the same at both endpoints, indicating no net change.
Step-by-step explanation:
The question asks us to find the value of the integral of f''(x) from 1 to 4, which can be approached using the Fundamental Theorem of Calculus. Since f'(x) represents the derivative of f(x), the integral of f''(x) from 1 to 4 will give us the change in f'(x) over that interval, which is f'(4) - f'(1). Given that f'(1) = 3 and f'(4) = 3, the change is 3 - 3 = 0. Hence, the integral ∫_1^4 f''(x) dx = 0.