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Response Details:
Of F(x), F’(x), and F’’(x), only F'(x) is negative. F(x) cannot take on any negative values, based on the problem, so F(x) is positive everywhere. F'(x) is negative, since F(x) is decreasing everywhere (i.e. the slopes at every point of the function are negative, hence a negative fist derivative everywhere). Lastly, the function decreases rapidly in the beginning and then slower towards the end. So, this would be a concave up graph, which means the first derivative is increasing everywhere (i.e. the slopes are increasing as x increases). So, the second derivative is positive everywhere.
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