The local linear approximation of a function f will always be greater than or equal to the function's value if, for all x in an interval containing the point of tangency, f''0?

Question

The local linear approximation of a function f will always be greater than or equal to the function's value if, for all x in an interval containing the point of tangency, 
f''<0 or f''>0?

anonymous · Answer

Just think about if for a bit....

anonymous · Answer

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anonymous · Answer

In this case we know that the linear approximation is greater than or equal.

anonymous · Answer

What if $f''$?

anonymous · Answer

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Is the slope going down or is it going up as x increases?

=)