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Then given any path [x(t), v(t)], the action S of that path is the integral of the Lagrangian over time:
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The constant b has no effect on the slope of the line, so we can ignore it. And the constant a just is the slope: If we change x by an amount Δx, then f (x) changes by aΔx, so Δf (x)/Δx=a, no matter what x itself is. We therefore have
