Question

30 points! Inflection points question. Okay, so I know that an inflection point is where the function is continuous and the concavity changes. On the graph I attached, it is asking to: "Use the graph of f "(x) below to state x-coordinates of the inflection points for the graph of f(x)."

Am I supposed to find the concavity changes of f(x) or of f"(x)? Also, do I give the x coordinate or the y coordinate when writing my answer.

Answer 1

Find the concavity changes of f(x).
Give the x-coordinates.

So, the answer to the multiple choice question is -1 and 5 since those points are where f''(x) changes sign.

Note: You can tell that you're supposed to find the concavity changes of f(x) and not f''(x) because from the graph it's obvious that the concavity of f"(x) doesn't change.