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?

Answer 1

Just think about if for a bit....

Answer 2

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

Answer 3

What if \(f''\)?

Answer 4

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

=)