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sbart
02-26-2012, 04:16 PM
Consider the odd function f that is continuous,differentiable, and has the function values shown in the table.





x


-5


-4


-1


0


2


3


6




f(x)


1


3


2


0


-1


-4


0






(a) Determine f (4).

(b) Determine f (-3).

(c) Plot the points and make a possible sketch of the graph off on the interval [-6,6]. What is the smallest critical number of critical points in the interval? Explain.


(d) Does there exist at least one real number c in the interval (-6,6) where f '(c) = -1? Explain.


(e) Is it possible that http://s3.amazonaws.com/answer-board-image/cramster-equation-2007541516156331388857539750007760.giff (x) does not exist? Explain.

(f) Is it necessary that f '(x) exists at x = 2? Explain.

I've completed a, b, and c, but I don't know how to explain the rest. Thanks for any help anyone can lend!

pka
02-26-2012, 04:52 PM
Consider the odd function f that is continuous,differentiable, and has the function values shown in the table.



x


-5


-4


-1


0


2


3


6




f(x)


1


3


2


0


-1


-4


0








(d) Does there exist at least one real number c in the interval (-6,6) where f '(c) = -1? Explain.
(e) Is it possible that http://s3.amazonaws.com/answer-board-image/cramster-equation-2007541516156331388857539750007760.giff (x) does not exist? Explain.

(f) Is it necessary that f '(x) exists at x = 2? Explain.

d) Use the mean value theorem
\dfrac{f(2)-f(-1)}{2-(-1)}=~?


(e) Note that f is continuous. What does that have to do with limits?

You think about (f).