Using Linear Approximation, estimate $f$ for a change in $x$ from $x=a$ to $x=b.$

$f(x)=x^{\frac{1}{4}},a=81,b=81\mathrm{.}4$

Consider the work to estimate $f.$

$f^{\text{'}}(x)=\frac{1}{4}{x}^{-\frac{3}{4}}$

$f^{\text{'}}(a)=\frac{1}{4}*{81}^{-\frac{3}{4}}=\frac{1}{108}$

$f$~~$f^{\text{'}}(a)x=\frac{1}{108}(-0\mathrm{.}4)=-0\mathrm{.}00370$

Identify the first error in the estimate of $f.$

The value of $f^{\text{'}}(a)$ should be $f^{\text{'}}(a)=6\mathrm{.}75.$

The change in $x$ should be $x=0\mathrm{.}4.$

The value of $f^{\text{'}}(a)$ should be $f^{\text{'}}(a)=-6\mathrm{.}75.$

The derivative of $f$ should be $x^{-\frac{3}{4}}.$

The derivative of $f$ should be $\frac{1}{4}{x}^{\frac{3}{4}}.$Using Linear Approximation, estimate $f.$

$($Use decimal notation. Give your answer to five decimal places.$)$

Use a calculator to compute the error in the Linear Approximation.

$($Use decimal notation. Give your answer to five decimal places.$)$

error ~~ $$

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I really need the most help answering the last part of the question, the part about computing the error in the linear approximation. Thank you!