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Find the linearization L(x) of the function at a. f(x) = x, a = 9
Solution:
Given, the function f(x) = x
We have to find the linearization L(x) of the function at a = 9.
Using the formula,
L(x) = f(a) + f’(a)(x - a)
Now,
f(x) = x
f(a) = f(9) = 9
f’(x) = 1
f’(a) = f’(9) = 1
Substituting the values of f(a) and f’(a), the function becomes
L(x) = 9 + 1(x - 9)
Therefore, the linearization of f(x) = x at a = 9 is L(x) = 9 + 1(x - 9).
Find the linearization L(x) of the function at a. f(x) = x, a = 9
Summary:
The linearization of the function f(x) = x at a = 9 is L(x) = 9 + 1(x - 9).
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