Mathematics: Find the linear approximation of the function f(x) = 4 − x at a = 0. L(x) = $$ Incorrect: Your answer is incorrect. Use L(x) to approximate the numbers 3.9 and 3.99 . (Rou

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Find the linear approximation of the function f(x)

chanevelyn2

30.01.2022

L(x)=4-x

$L(3.9)=0.1\\L(3.99)=0.01$

Step-by-step explanation:

The linear approximating polynomial is: L(x) = f(a) + f'(a)(x - a)

Given: f(x) = 4 - x at a=0

f(0)=4-0=4

f'(x)=-1, Therefore: f'(a)=-1

Therefore, the linear approximation of f(x) at a=0 is:

$L(x) = f(0) + f'(a)(x - 0)\\L(x)=4-x$

We then use our result to approximate 3.9 and 3.99.

$L(3.9)=4-3.9=0.1\\L(3.99)=4-3.99=0.01$

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