Linearization At a Point

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