Please help me with steps. Please see the attached file.
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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.
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.