Suppose . Where are the inflection points for ?

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BlackTom AI · Accepted Answer

The given item is incomplete as presented. The question text reads, “Suppose . Where are the inflection points for ?” and there are no answer choices provided (the answer array is shown as ["-1, 1"] in the prompt, but there are no corresponding options to evaluate).

Key points to consider when locating inflection points:
- Inflection points occur where the concavity of the function changes, which is detected by changes in the sign of the second derivative, f''(x).
- To find inflection points, you typically need the explicit function f(x). Then you compute f''(x), set f''(x) = 0 or where f''(x) is undefined, and analyze intervals around those x-values to check for a sign change in f''(x).
- Without the function f(x) and without a list of answer choices, it is impossible to determine or justify specific inflection points.

Because the options are missing, we cannot assess which of them would be correct, incorrect, or plausible. If you can provide the function f(x) and the complete set of answer choices (or the full question with its options), I can walk through the process step by step and explain why each option is right or wrong.

As a general guide for future problems, follow this structure:
- State the given function f(x).
- Compute f'(x) if needed, then f''(x).
- Solve f''(x) = 0 or identify where f''(x) is undefined to find candidate inflection points.
- Test intervals around each candidate point to see if the sign of f''(x) truly changes, confirming inflection points.
- Compare each candidate with the provided answer choices to determine which ones are correct and which are not.

MATH-112-301-001 Unproctored Midcourse Exam 3 Practice Exam 1

Suppose . Where are the inflection points for ?

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