The graphs of a function f(x) and its derivative f'(x) can give several pieces of information. The value of f'(x) is the slope of the tangent line to f(x) at that point, and varies depending on x. It is positive if the graph of f(x) is increasing, and negative if f(x) is decreasing. The graph of f'(x) intersects the x-axis at the local maxima and minima of f(x), where the slope of f(x) = 0. If f(x) changes concavity — that is, if f(x) is concave up over the interval a→b and concave down over b→c (or vice versa) — then x = b is an inflection point. The First and Second Derivative Tests allow the formation of a rough sketch of f(x), based on the values of f'(x) over given intervals.
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