Whether the statement, if , then f has a local maximum or minimum at c is true or false.
The given statement is false.
If then the tangent line of f will be parallel to the x-axis and it does not guarantee of the existence of local maximum or local minimum.
For example, consider the function .
Differentiate with respect to x.
Set to obtain,
For all non-zero values of x, is increasing thus is an inflection point but not local maximum or minimum.
Therefore, the given statement is false.
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