Question

Write the equation of the line that represents the linear approximation to the following function at the given point a. b. Use the linear approximation to estimate the given quantity. c. Compute the percent error in the​ approximation, ​, where the exact value is given by a calculator. at a​0; ​f(​) a.​ L(x) nothing

Answer 1

Answer:

(a) 15 - 4x

(b) 6.6

(c) 5.7143%

Step-by-step explanation:

The given problem is incomplete. Please find attachment of the complete description.

According to the question:

$f(x)=11-x^2$

now,

(a)

$f(a)=11-2^2$

       $=7$

$f'(x)=-2x$

$f'(2)=-4$

$f(x)=f(a)+f'(a)(x-a)$

       $=7-4(x-2)$

       $=7-4x+8$

       $=15-4x$

(b)

$f(2.1)=15-4\times 2.1$

         $=6.6$

(c)

$Error=\frac{100\times \left | 6.6-7 \right |}{7}$

          $=5.7143$%