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

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- Sep 23rd 2010, 09:23 PMmelliepDerivatives 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, 09:45 PMTheCoffeeMachine
- Sep 23rd 2010, 10:15 PMmelliep
And if someone does reply, could you please tell me why you got the answer you did?

Thank you. - Sep 24th 2010, 06:42 PMTikoloshe
Unless you are missing some more information, they all seem possible (except of course d). The local behavior of a function over $\displaystyle \mathbb{R}$ does not determine its global behavior (this is different for a holomorphic complex functions).

So the answer is that $\displaystyle f(6)$ could be anything. - Sep 25th 2010, 03:49 AMHallsofIvy
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, 06:27 PMTikoloshe