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Section 4.7 - Approximations 3.6 T4. Linearization of a Function at a Point x = a f(x) (a, f(a)) f(x) – f(a) = f ’(a)(x – a) Linearization Demonstration.

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Presentation on theme: "Section 4.7 - Approximations 3.6 T4. Linearization of a Function at a Point x = a f(x) (a, f(a)) f(x) – f(a) = f ’(a)(x – a) Linearization Demonstration."— Presentation transcript:

1 Section Approximations 3.6 T4

2

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

4 Find the equation of the line tangent to

5 Use the linearization of to find f(2.1)

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

7 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, a)f ‘ < 0 b)f ‘ > 0 c)f” < 0 d)f” > 0 e)f ‘ = f “ = 0


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