Find the linearization L(x) of f(x) at x = a.
-$$f ( x ) = \sqrt [ 3 ] { x } , a = 8$$
A) $L ( x ) = \frac { 1 } { 12 } x + \frac { 4 } { 3 }$
B) $L ( x ) = \frac { 1 } { 12 } x + \frac { 2 } { 3 }$
C) $L ( x ) = \frac { 1 } { 4 } x + 4$
D) $L ( x ) = \frac { 1 } { 4 } x + \frac { 2 } { 3 }$

Question

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 $f(x) = \sqrt[3]{x}$, $f'(x) = \frac{1}{3}x^{-\frac{2}{3}}$. At $x = 8$, $f(8) = 2$ and $f'(8) = \frac{1}{12}$. Thus, $L(x) = 2 + \frac{1}{12}(x - 8) = \frac{1}{12}x + \frac{4}{3}$.

Find the Linearization L(x) of F(x) at X = A f(x)=x3,a=8f ( x ) = \sqrt [ 3 ] { x } , a = 8f(x)=3x​,a=8

Find the Linearization L(x) of F(x) at X = A $f ( x ) = \sqrt [ 3 ] { x } , a = 8$