Question

True or False, If f'(1)= f''(1) = 0, then x = 1
MUST be an inflection point.(Remember to give your reasons in the written section. Feel free to give examples to support your answer as well.)
Responses

True
False

Answer 1

Answer:

False

Step-by-step explanation:

For a point to be an inflection point, two conditions must be met: the second derivative must exist, and there must be a change in concavity at that point. The given information only tells us that the first and second derivatives are both 0 at x = 1, but it does not guarantee a change in concavity.