Whether the statement, if then is an inflection point of the curve is true or false.
The given statement is false.
Inflection point occurs at only if the following conditions are satisfied.
1) The function f must be continuous at
2) The second derivative must change its sign.
The given statement is false since the following example disproves the given statement.
Consider a function, .
Differentiate with respect to x.
Find the second derivative of .
Substitute in .
Thus, do not changes its sign.
Hence, is not an inflection point.
Therefore, the given statement is false.
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