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**Section 4.7 - Approximations**

3.6 T4

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**Linearization of a Function at a Point x = a**

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

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**Find the equation of the line tangent to**

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**Use the linearization of**

to find f(2.1)

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**Find f(-3.1) using the local linearization of**

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**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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