# Math Help - local linear approximation

1. ## local linear approximation

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,

A) f'<0
B) f'>0
C) f''<0
D) f''>0
E) f'=f''=0

2. $f''(x)<0$ means that the graph is always concave down. Looking at the graph will probably give you an idea why all linear approximations on such function are always larger or equal to the function.

3. so C is the correct the answer?

4. Originally Posted by DINOCALC09
so C is the correct the answer?
I don't know. I gave you a graph to help you focus on a choice. Do you know what $f''(x)<0$ means? Do you know what a local linear approximation would look like? Did you completely understand the question?

5. yes, f''(x) is the 2nd derivative

6. ok the answer is B. thank you