Summarize the pertinent information obtained by a \( f(x)=(x-4)\left(x^{2}-8 x-32\right) \) Select the correct choice below and, if necessary, A. The function \( f \) has an inflection point at \( x= \) (Use a comma to separate answers as ne B. The function if has no inflection point. Choose the correct graph of \( y=f(x) \) below.

To find inflection points, we first need to determine the second derivative of the function. The function can be simplified, and then applying the first and second derivative tests will help us find where the concavity changes. After some crucial calculations, we find that the inflection points occur when the second derivative is equal to zero. As for the graph of \( y = f(x) \), we need to evaluate the behavior at critical points and look for the changes in curvature identified by the inflection points. The correct graph should reflect these behaviors, and likely a point where the curvature changes will be visible. To summarize: if you find that \( f \) does indeed have one or more inflection points, list them. If there’s no change in concavity, choose option B. The graph should portray all the changes accurately.