attempt 1: 10 attempts remaining. suppose that f(6)= -7 and f(6)=1. a. write a linearization for f with…

attempt 1: 10 attempts remaining. suppose that f(6)= -7 and f(6)=1. a. write a linearization for f with respect to x. fl(x)= b. use the linearization to estimate f for x = 6.5. fl(6.5)=

attempt 1: 10 attempts remaining. suppose that f(6)= -7 and f(6)=1. a. write a linearization for f with respect to x. fl(x)= b. use the linearization to estimate f for x = 6.5. fl(6.5)=

Answer

Explanation:

Step1: Recall linearization formula

The linearization formula of a function $y = f(x)$ at $x = a$ is $f_L(x)=f(a)+f^{\prime}(a)(x - a)$. Here $a = 6$, $f(6)=-7$ and $f^{\prime}(6)=1$.

Step2: Write the linearization for part a

Substitute $a = 6$, $f(6)=-7$ and $f^{\prime}(6)=1$ into the formula: $f_L(x)=-7 + 1\times(x - 6)=x-13$.

Step3: Estimate for part b

Substitute $x = 6.5$ into $f_L(x)$: $f_L(6.5)=6.5-13=-6.5$.

Answer:

a. $f_L(x)=x - 13$ b. $f_L(6.5)=-6.5$