Consider the odd function that is continuous and

Authors:

Ron Larson, Bruce H.edwards

Chapter:

Applications Of Differentiations

Exercise:

3. Review Exercises

Question:2 | ISBN:9780547167022 | Edition: 9

Question

Consider the odd function $f$ that is continuous and differentiable and has the functional 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 of $f$ on the interval $f\left [ -6, 6 \right ]$ . What is the smallest number of critical points in the interval? Explain.

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

(e) Is it possible that $\lim_{x\rightarrow 0}f(x)$ does not exist? Explain.

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

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