The blue line is f(x); the faint purple line is the derivative f′(x). Notice: f′ crosses 0 exactly at the peaks/troughs of f. The tangent (red) gives the slope; the shaded region (green) is the ∫ area.
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Drag on the graph = move the study point · change the function & mode on the right · try "Limit h→0"
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f(x) and its derivative f′(x) vs x (f′ = the slope of f)f(x)f′(x)