11. given the graph of f below, at which values of x do points of inflection occur?
11. given the graph of f below, at which values of x do points of inflection occur?
Answer
Explanation:
Step1: Recall inflection - point definition
A point of inflection is a point where the concavity of the function changes, i.e., the second - derivative $f''(x)$ changes sign. Geometrically, it is a point where the graph of the function changes from being concave up to concave down or vice - versa.
Step2: Analyze the graph
Looking at the graph of $y = f(x)$, we observe the changes in concavity. The graph changes from concave up to concave down or vice - versa at points $b$, $d$, and $g$.
Answer:
$x = b$, $x = d$, $x = g$