Find the linearization L(x) of f(x) at x = a.
-$f ( x ) = x + \frac { 1 } { x } , a = 3$
A) $L ( x ) = \frac { 10 } { 9 } x + \frac { 2 } { 3 }$
B) $L ( x ) = \frac { 8 } { 9 } x + \frac { 1 } { 2 }$
C) $ L ( x ) = \frac { 10 } { 9 } x + \frac { 1 } { 2 }$
D) $L ( x ) = \frac { 8 } { 9 } x + \frac { 2 } { 3 }$

Question

Quizplus · Accepted Answer

To find the linearization at x = a:
1. Find f(a) = a + 1/a = 3 + 1/3 = 10/3
2. Find f'(x) = 1 - 1/x^2
3. Evaluate f'(a) = 1 - 1/3^2 = 8/9
4. Use the following formula: L(x) = f(a) + f'(a)*(x-a)
L(x) = 10/3 + (8/9)*(x-3) = (80/27 + 9x)/9, which simplifies to L(x) = (8/9)x + 2/3. Therefore, the correct choice is D.

Find the Linearization L(x) of F(x) at X = A f(x)=x+1x,a=3f ( x ) = x + \frac { 1 } { x } , a = 3f(x)=x+x1​,a=3

Find the Linearization L(x) of F(x) at X = A $f ( x ) = x + \frac { 1 } { x } , a = 3$