Whether the statement, if f has an absolute minimum value at c then is true or false.
The given statement is false.
The given statement as the below example disproves the given statement.
Consider the function, .
As f is always non-negative function it has absolute minimum at .
But derivative of the function does not exist at
Calculate the derivative of as follows.
Thus the left hand limit is not same as the right hand limit.
So, does not exist.
Therefore, the given statement is false.
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