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Understanding Linearization in Calculus

Learn how to calculate linearization of a function at a point, apply it to find values, and understand local linear approximation principles effectively.

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Understanding Linearization in Calculus

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  1. Linearization At a Point

  2. f(x) Linearization of a Function at a Point x = a (a, f(a)) f(x) – f(a) = f ’(a)(x – a)

  3. Use the linearization of to find f(2.1)

  4. Find f(-3.1) using the linearization of

  5. Use the linearization of at x = 8 to find f(8.1)

  6. 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

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