# Derivatives and Second Derivatives

• Sep 23rd 2010, 10:23 PM
melliep
Derivatives and Second Derivatives
A function f satisfies the following conditions...
f(4) = 28
f '(4) = 3
f ''(x) < 0 for x >or= 4

Which of the following are possible values for f(6)? (Select all that apply.)
a. 31
b. 34
c. 37
d. None of these
• Sep 23rd 2010, 10:45 PM
TheCoffeeMachine
Quote:

Originally Posted by melliep
f ''(x) < 0 for x 4

For $x\;\;?\;\;4$? Something is missing here.
• Sep 23rd 2010, 11:15 PM
melliep
And if someone does reply, could you please tell me why you got the answer you did?

Thank you.
• Sep 24th 2010, 07:42 PM
Tikoloshe
Unless you are missing some more information, they all seem possible (except of course d). The local behavior of a function over $\mathbb{R}$ does not determine its global behavior (this is different for a holomorphic complex functions).

So the answer is that $f(6)$ could be anything.
• Sep 25th 2010, 04:49 AM
HallsofIvy
Good point but not quite correct. We are given some "global" information- we are told that f"(x) < 0 for all x> 4. Therefore f' is less than 3 for x> 4 and so the graph of f(x) is below the tangent line at x= 4. That tangent line is y= 3(x- 4)+ 28 and when x= 6 that gives 6+ 28= 34. f(6) must be less than 34.
• Sep 25th 2010, 07:27 PM
Tikoloshe
Quote:

Originally Posted by HallsofIvy
Good point but not quite correct. We are given some "global" information- we are told that f"(x) < 0 for all x> 4.

Yes, thank you of course you are right. I seem to have mis-read the post.