Find the linearization L(x) of f(x) at x = a.
-$$f ( x ) = \frac { x } { 3 x + 7 } , a = 0$$
A) $L ( x ) = - \frac { 1 } { 7 } x$
B) $L ( x ) = \frac { 1 } { 7 } x$
C) $L ( x ) = - \frac { 1 } { 49 } x$
D) $L ( x ) = \frac { 1 } { 49 } x$

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)

where f'(a) is the derivative of the function evaluated at x=a.

In this case, we have:

f(x) = x / (3x + 7)

f'(x) = (3) / (3x + 7)^2

So, when a=0, we have:

f(0) = 0 / (3(0) + 7) = 0/7 = 0

f'(0) = (3) / (3(0) + 7)^2 = 3/49

Therefore, the linearization is:

L(x) = f(0) + f'(0)(x-0) = 0 + (3/49)x = (1/7)x

Hence, the answer is B.

Find the Linearization L(x) of F(x) at X = A f(x)=x3x+7,a=0f ( x ) = \frac { x } { 3 x + 7 } , a = 0f(x)=3x+7x​,a=0

Find the Linearization L(x) of F(x) at X = A $f ( x ) = \frac { x } { 3 x + 7 } , a = 0$