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The average gradient between two points (x1, y1) and (x2, y2) is the slope of the secant line connecting them, calculated as m = (y2 − y1)/(x2 - x1). It represents the average rate
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The average gradient between two points and is the slope of the secant line connecting them, calculated as . It represents the average rate of change of a function over an interval.
The gradient at a point (also known as the instantaneous gradient or derivative) is the slope of the tangent line to the curve at that specific point. It represents the instantaneous rate of change of the function at that point and is found using differentiation, which can be derived from first principles: $f'(x) = \lim_{h \to 0} \frac{f(x+h) - f
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