Let odd function f which is continuous, differentiable and has function values given in table.
| x |
-5 |
-4 |
-1 |
0 |
2 |
3 |
6 |
| f(x) |
1 |
3 |
2 |
0 |
-1 |
-4 |
0 |
i) Find f (4).
ii) Find f (-3).
iii) Plot points and make possible sketch of graph off on interval [-6,6]. Find smallest critical number of critical points in interval? Describe.
iv) Does there exist at least one real number c in interval (-6,6) where f '(c) = -1? Describe.
v) Is it possible that limx→0f (x) doesn't exist? Describe.
vi) Is it necessary that f '(x) exists at x = 2? Describe.