# local linear approximation

• Feb 10th 2008, 01:06 PM
DINOCALC09
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
• Feb 10th 2008, 02:46 PM
wingless
$f''(x)<0$ 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.

http://img116.imageshack.us/img116/6928/graph2lu7.png
• Feb 10th 2008, 03:16 PM
DINOCALC09
so C is the correct the answer?
• Feb 10th 2008, 03:27 PM
wingless
Quote:

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?
• Feb 10th 2008, 03:33 PM
DINOCALC09
yes, f''(x) is the 2nd derivative
• Feb 10th 2008, 04:01 PM
DINOCALC09
ok the answer is B. thank you