If a continuous curve has inflection point at , which statement must be true regarding if it exists?
Answer and explanation
Correct answer: D.
- Step 1: By definition, an inflection point is a point where concavity changes sign.
- Step 2: If the second derivative exists and is continuous at an inflection point , it must equal zero ().
Answer
f''(c) = 0.
Why not the others: '' indicates concave upward; '' indicates concave downward; '' defines a critical point, not necessarily an inflection point.
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