14. given the graph of the derivative of f below, determine the interval(s) where the f is concave down.
14. given the graph of the derivative of f below, determine the interval(s) where the f is concave down.
Answer
Explanation:
Step1: Recall concavity - derivative relationship
A function $f(x)$ is concave down when $f''(x)<0$. Since the given graph is of $f'(x)$, we need to find where $f'(x)$ is decreasing because the derivative of $f'(x)$ is $f''(x)$. When $f'(x)$ is decreasing, $f''(x)<0$.
Step2: Analyze the graph of $f'(x)$
Looking at the graph of $f'(x)$, we see that $f'(x)$ is decreasing on the intervals $(a, b)$ and $(d, e)$.
Answer:
$(a, b)$ and $(d, e)$