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Linearization At a Point

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## Linearization At a Point

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**f(x)**Linearization of a Function at a Point x = a (a, f(a)) f(x) – f(a) = f ’(a)(x – a)**Use the linearization of**to find f(2.1)**Use the linearization of**at x = 8 to find f(8.1)**The local linear approximation of a function f will always**be greater • than or equal to the function’s value if, for all x in an interval • containing the point of tangency, • f ‘ < 0 • f ‘ > 0 • f” < 0 • f” > 0 • f ‘ = f “ = 0