Consider the odd function f that is continuous,differentiable, and has the function values shown in the table.
(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
f (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!
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
(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!