Concavity Problems

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Concavity Practice Problem 1
Problem: Determine where the given function is increasing and decreasing. Find where its graph is concave up and concave down. Find the relative extrema and inflection points and sketch the graph of the function. f(x)=x^5-5x Concavity Practice Problem 2
Problem: Use second derivative test to find the relative extrema and minima of the given function. f(x)=x+1/x Concavity Practice Problem 3
Problem: For f'(x)=x^2-2x-8: a) find the intervals on which f is increasing and decreasing b)find intervals on which the graph of f is concave up and concave down c) find the x coordinates of the relative extrema and inflection points of f d) sketch a possible graph for f(x). Concavity Practice Problem 4
Problem: Sketch a graph of the given function f(x)=x^4/3