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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.

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    https://brainmass.com/math/derivatives/functions-derivatives-172695

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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 ...

    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.

    $2.49

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