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An Introduction to Differentiation

The diagram contains a function f(x) and two points on that function A (which is fixed) and B (which is dynamic). There is a blue line representing the tangent at A and a maroon line represennting the secand AB.
Pay attention to the gradients of the lines - through the slope function on the secant AB and also through the two equations of the lines scnt and tgnt in the Algebra screen. What happens as point B gets closer to A and can you explain what happens to the equations when A and B lie on top of each other?