1. Section 4.7 - Approximations
3.6 T4

3. 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)

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,
f ‘ < 0
f ‘ > 0
f” < 0
f” > 0
f ‘ = f “ = 0