A plot overlaying a function and its tangent line at a specific point can visually demonstrate the concept of a derivative. For example, plotting the function $$u = f(x)$$ alongside its tangent line $$y = 2x - 3$$ at $$x=1$$ visually shows how the tangent line perfectly grazes the function's curve at that point, where the coefficient $$2$$ represents the slope of the tangent line.

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To compare multiple functions or datasets, multiple curves can be overlaid on a single matplotlib plot. A unified plotting utility can handle varying input shapes (such as 1D tensors or lists), iterate through multiple sets of $$x$$ and $$y$$ coordinates alongside their respective formatting strings, and plot them sequentially on the same axes before applying final axes configurations like labels and limits.

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