Question

use linear approximations to estimate the quantity. 4root 16.04

Answer 1

\[\sqrt[4]{16.04}\]

Answer 2

let \[f(x)=x^{1/4}\]

then \[L(x)=f(16)+f'(16)(x-16)\]

Answer 3

~\[\sqrt[4]{16}+\sqrt[4]{0.04}\]
\[=2+\sqrt[4]{{1}\over{25}}\]
\[=2+\sqrt{1\over5}\]
\[=2+ {√5 \over 5}\]
\[={10+√5 \over 5}\]

for some reason what ever i have done is terribly inaccurate

Answer 4

\[f'(x)=\frac{1}{4}x^{-3/4}\]
\[f'(16)=\frac{1}{4}16^{-3/4}=\frac{1}{4}2^{-3}=\frac{1}{4}\frac{1}{8}=\frac{1}{32}\]
\[L(x)=f(16)+f'(16)(x-16)=2+\frac{1}{32}(x-16)\]

\[L(16.04)=2+\frac{1}{32}(16.04-16)=2+\frac{1}{32}\cdot .04=2.00125\]