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MMLU-Pro / 7739 / Which statement is true?

Problem

Answer published by the source. Consult the official source to check your work against its answer.

question

Which statement is true?

category

math

options

  1. If f′(c) ≠ 0, then f has a local maximum or minimum at (c, f(c)).
  2. If f′(c) = 0, then f has a local maximum or minimum at (c, f (c)).
  3. If f is differentiable at x = c, then f is continuous at x = c.
  4. If f(x) is discontinuous at x = c, then f might be differentiable at x = c.
  5. If f is differentiable at x = c, then f′(c) might or might not exist.
  6. If f(x) is continuous at x = c, then the graph of f has a minimum or maximum at (c, f(c)).
  7. If f(x) is continuous at x = c, then f′(c) exists.
  8. If f′′(c) = 0, then the graph of f has an inflection point at (c, f (c)).
  9. If f′(c) = 0, then f(x) is constant for all x.
  10. If f′′(c) ≠ 0, then the graph of f has an inflection point at (c, f(c)).

src

ori_mmlu-high_school_mathematics

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Source and history

upstream_id / Original problem ID
7739
task_id
4c556565-2923-5785-87d5-8957f507222e
task_key
default--test--7739
task_revision_id
1
config / split
default / test

Official source

initial import