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Tangent and perpendicular

The model demonstrates tangent and perpendicular to a graph at a point.

Consider a function f(x). A tangent to f(x) at a point x0 is a line y = f(x0)+ f `(x0)(x-x0). A normal to f(x) at the x0 is line y = f(x0)+(x-x0)/f `(x0). The normal is a perpendicular to f(x).

You may enter a function f(x) in the text field and choose a x0. The y0=f(x0), tangent and normal at this point are calculated automatically in analytical form. The graph of the f(x) is blue, the tangent is a green line, the normal is a red line.

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