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# Functions and derivatives

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1. Does there exist a differentiable function f so that f(-3) = -2, f(1) = -6, and f ' (x) > 0 for all x?
2. Find all numbers c in the interval (1,2) that satisfy the conclusion of the mean-value theorem.

3. Give the values of x for which the function graphed below is increasing.

4. The graph of f ' is shown below. Give the values of x for which the graph of f is concave down.

5. The graph of f ' is shown below. Give the values of x for which the graph of f is concave up.

##### Solution Summary

This shows how to determine if there exists a differentiable function for a given situation, find numbers that satisfy mean-value theorem, and give values for whether a graph is increasing, concave down, or concave up.

##### Solution Preview

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Problem #1
The answer is NO.
If it exist, according to the Mean Value Theorem, there exists some , such that and it ...

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