attempt 1: 10 attempts remaining. suppose that f(12)=19 and f(12)= - 0.8999999999999999. a. write a…

attempt 1: 10 attempts remaining. suppose that f(12)=19 and f(12)= - 0.8999999999999999. a. write a linearization for f with respect to x. fl(x)= b. use the linearization to estimate f for x = 12.1. fl(12.1)=

attempt 1: 10 attempts remaining. suppose that f(12)=19 and f(12)= - 0.8999999999999999. a. write a linearization for f with respect to x. fl(x)= b. use the linearization to estimate f for x = 12.1. fl(12.1)=

Answer

Explanation:

Step1: Recall linear - approximation formula

The linearization of a function $y = f(x)$ at $x = a$ is given by $f_L(x)=f(a)+f^{\prime}(a)(x - a)$. Here $a = 12$, $f(12)=19$ and $f^{\prime}(12)=- 0.9$ (approx). So $f_L(x)=19-0.9(x - 12)$.

Step2: Expand the linear - approximation formula

$f_L(x)=19-0.9x+10.8=29.8 - 0.9x$.

Step3: Estimate $f(12.1)$

Substitute $x = 12.1$ into $f_L(x)$. $f_L(12.1)=29.8-0.9\times12.1$. $f_L(12.1)=29.8 - 10.89=18.91$.

Answer:

a. $f_L(x)=29.8 - 0.9x$ b. $f_L(12.1)=18.91$