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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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