Find the linearization L(x) of f(x) at x = a.
-f(x) = cos x, a = 0
A) L(x) = -1
B) L(x) = 0
C) L(x) = 1
D) L(x) = 4x + 1

Name: Find the linearization L(x) of f(x) at x = a. -f(x) = cos x, a = 0 A) L(x) = -1 B) L(x) = 0 C) L(x) = 1 D) L(x) = 4x + 1
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Quizplus · Accepted Answer

The linearization of a function $f(x)$ at $x = a$ is given by $L(x) = f(a) + f'(a)(x - a)$. For $f(x) = \cos(x)$ at $a = 0$, $f(a) = \cos(0) = 1$ and $f'(x) = -\sin(x)$, so $f'(a) = -\sin(0) = 0$. Thus, $L(x) = 1 + 0(x - 0) = 1$.

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