Question(7 pts) Let $f(x)$ be a twice differentiable function and the graph of the derivative $f^{\prime}(x)$ is given below. i) $f(x)$ is increasing on the interval $(1,2)$. ii) $f(x)$ is decreasing on the interval $(2,5)$. iii) $(5, f(5))$ is a critical point of $f(x)$. iv) $(3.5, f(3.5))$ is an inflection point of $f(x)$.
Choose all the correct statements

Studdy Solution
An inflection point occurs where the concavity changes, which is indicated by a change in the sign of $f''(x)$ or where $f'(x)$ changes from increasing to decreasing or vice versa.
The graph shows a change in the slope of $f'(x)$ at $x = 3.5$, indicating an inflection point at $(3.5, f(3.5))$.
The correct statements are: i) $f(x)$ is increasing on the interval $(1,2)$. ii) $f(x)$ is decreasing on the interval $(2,5)$. iii) $(5, f(5))$ is a critical point of $f(x)$. iv) $(3.5, f(3.5))$ is an inflection point of $f(x)$.
All statements are correct.